Essay – Athlete’s high salaries. Should they be paid that amount or not?

Essay – Athlete’s high salaries. Should they be paid that amount or not?

Athlete’s high salaries: Should they be paid that amount or … Read More...
Statistical Methods (STAT 4303) Review for Final Comprehensive Exam Measures of Central Tendency, Dispersion Q.1. The data below represents the test scores obtained by students in college algebra class. 10,12,15,20,13,16,14 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) Q.2. The data below represents the test scores obtained by students in English class. 12,15,16,18,13,10,17,20 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) (f) Compare the results of Q.1 and Q.2, Which scores College Algebra or English do you think is more precise (less spread)? Q.3 Following data represents the score obtained by students in one of the exams 9, 13, 14, 15, 16, 16, 17, 19, 20, 21, 21, 22, 25, 25, 26 Create a frequency table to calculate the following descriptive statistics (a) mean (b) median (c) mode (d) first and third quartiles (e) Construct Box and Whisker plot. (f) Comment on the shape of the distribution. (g) Find inter quartile range (IQR). (h) Are there any outliers (based on IQR technique)? In the above problem, if the score 26 is replaced by 37 (i) What will happen to the mean? Will it increase, decrease or remains the same? (j) What will be the new median? (k) What can you say about the effect of outliers on mean and median? Q.4 Following data represents the score obtained by students in one of the exams 19, 14, 14, 15, 17, 16, 17, 20, 20, 21, 21, 22, 25, 25, 26, 27, 28 Create a frequency table to calculate the following descriptive statistics a) mean b) median c) mode d) first and third quartiles e) Construct Box and Whisker plot. f) Comment on the shape of the distribution. g) Find inter quartile range (IQR). h) Are there any outliers (based on IQR technique)? In the above problem, if the score 28 is replaced by 48 i) What will happen to the mean? Will it increase, decrease or remains the same? j) What will be the new median? k) What can you say about the effect of outliers on mean and median? Q.5 Consider the following data of height (in inch) and weight(in lbs). Height(x) Frequency 50 2 52 3 55 2 60 4 62 3  Find the mean height.  What is the variance of height? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.6. The following table shows the number of miles run during one week for a sample of 20 runners: Miles Mid-value (x) Frequency (f) 5.5-10.5 1 10.5-15.5 2 15.5-20.5 3 20.5-25.5 5 25.5-30.5 4 (a) Find the average (mean) miles run. (Hint: Find mid-value of mile range first) (b) What is the variance of miles run? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.7. (a) If the mean of 20 observations is 20.5, find the sum of all observations? (b) If the mean of 30 observations is 40, find the sum of all observations? Probability Q.8 Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. a) How many students are in both classes? b) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? Q.9 A drawer contains 4 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and then replaced. Another ball is taken from the drawer. What is the probability that (Draw tree diagram to facilitate your calculation). (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q.10 A drawer contains 3 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and not replaced. Another ball is then taken from the drawer. Draw tree diagram to facilitate your calculation. What is the probability that (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q. 11 Missile A has 45% chance of hitting target. Missile B has 55% chance of hitting a target. What is the probability that (i) both miss the target. (ii) at least one will hit the target. (iii) exactly one will hit the target. Q. 12 A politician from D party speaks truth 65% of times; another politician from rival party speaks truth 75% of times. Both politicians were asked about their personal love affair with their own office secretary, what is the probability that (i) both lie the actual fact . (ii) at least one will speak truth. (iii) exactly one speaks the truth. (iv) both speak the truth. Q.13 The question, “Do you drink alcohol?” was asked to 220 people. Results are shown in the table. . Yes No Total Male 48 82 Female 24 66 Total (a) What is the probability of a randomly selected individual being a male also drinks? (b) What is the probability of a randomly selected individual being a female? (c) What is the probability that a randomly selected individual drinks? (d) A person is selected at random and if the person is female, what is the probability that she drinks? (e) What is the probability that a randomly selected alcoholic person is a male? Q.14 A professor, Dr. Drakula, taught courses that included statements from across the five colleges abbreviated as AH, AS, BA, ED and EN. He taught at Texas A&M University – Kingsville (TAMUK) during the span of five academic years AY09 to AY13. The following table shows the total number of graduates during AY09 to AY13. One day, he was running late to his class. He was so focused on the class that he did not stop for a red light. As soon as he crossed through the intersection, a police officer Asked him to stop. ( a ) It is turned out that the police officer was TAMUK graduate during the past five years. What is the probability that the Police Officer was from ED College? ( b ) What is the probability that the Police Officer graduated in the academic year of 2011? ( c ) If the traffic officer graduated from TAMUK in the academic year of 2011(AY11). What is the conditional probability that he graduated from the ED college? ( d ) Are the events the academic year “AY 11” and the college of Education “ED” independent? Yes or no , why? Discrete Distribution Q.15 Find k and probability for X=2 and X=4. X 1 2 3 4 5 P(X=x) 0.1 3k 0.2 2k 0.2 (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers.What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Q.16 Find k. X 3 4 5 6 7 P(X=x) k 2k 2k k 2k (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers. What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Binomial Distribution: Q.17 (a) Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover? (b) A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of (i) more than 2 hits? (ii) at least 3 misses? (c) which of the following are binomial experiments? Explain the reason. i. Telephone surveying a group of 200 people to ask if they voted for George Bush. ii. Counting the average number of dogs seen at a veterinarian’s office daily. iii. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time. iv. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.” Normal Distribution Q.18 Use standard normal distribution table to find the following probabilities: (a) P(Z<2.5) (b) P(Z< -1.3) (c) P(Z>0.12) (d) P(Z> -2.15) (e) P(0.11<Z<0.22) (f) P(-0.11<Z<0.5) Q.19. Use normal distribution table to find the missing values (?). (a) P(Z< ?)=0.40 (b) P(Z< ?)=0.76 (c) P(Z> ?)=0.87 (d) P(Z> ?)=0.34 Q.20. The length of life of certain type of light bulb is normally distributed with mean=220hrs and standard deviation=20hrs. (a) Define a random variable, X A light bulb is randomly selected, what is the probability that (b) it will last will last more than 207 hrs. ? (c) it will last less than 214 hrs. (d) it will last in between 199 to 207 hrs. Q.21. The length of life of an instrument produced by a machine has a normal distribution with a mean of 22 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last (a) less than 10 months. (b) more than 28 months (c) between 10 and 28 months. Distribution of sample mean and Central Limit Theorem (CLT) Q.22 It is assumed that weight of teenage student is normally distributed with mean=140 lbs. and standard deviation =15 lbs. A simple random sample of 40 teenage students is taken and sample mean is calculated. If several such samples of same size are taken (i) what could be the mean of all sample means. (ii) what could be the standard deviation of all sample means. (iii) will the distribution of sample means be normal ? (iv) What is CLT? Write down the distribution of sample mean in the form of ~ ( , ) 2 n X N   . Q.23 The time it takes students in a cooking school to learn to prepare seafood gumbo is a random variable with a normal distribution where the average is 3.2 hours and a standard deviation of 1.8 hours. A sample of 40 students was investigated. What is the distribution of sample mean (express in numbers)? Hypothesis Testing Q.24 The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203 with standard deviation of 37. Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: n=3,00, =200.3. Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring (means does the result form current examination differs from 2002 report)?? (Follow the steps below to reach the conclusion) (i) Define null and alternate hypothesis (Also write what is  , and x in words at the beginning) (ii) Identify the significance level ,  and check whether it is one sided or two sided test. (iii) Calculate test statistics, Z. (iv) Use standard normal table to find the p-value and state whether you reject or accept (fail to reject) the null hypothesis. (v) what is the critical value, do you reject or accept the H0. (vi) Write down the conclusion based on part (iv). Q.25 A sample of 145 boxes of Kellogg’s Raisin Bran contain in average 1.95 scoops of raisins. It is known from past experiments that the standard deviation for the number of scoops of raisins is 0.25. The manufacturer of Kellogg’s Raisin Bran claimed that in average their product contains more than 2 scoops of raisins, do you reject or accept the manufacturers claim (follow all five steps)? Q.26 It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg. The standard deviation from the population is 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population? Use 10% level of significance. Q.27 A CEO claims that at least 80 percent of the company’s 1,000,000 customers are very satisfied. Again, 100 customers are surveyed using simple random sampling. The result: 73 percent are very satisfied. Based on these results, should we accept or reject the CEO’s hypothesis? Assume a significance level of 0.05. Q.28 True/False questions (These questions are collected from previous HW, review and exam problems, see the previous solutions for answers) (a) Total sum of probability can exceed 1. (b) If you throw a die, getting 2 or any even number are independent events. (c) If you roll a die for 20 times, the probability of getting 5 in 15th roll is 20 15 . (d) A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. Probability that he gets the first question right is 2 1 . (e) Typing in laptop and writing emails using the same laptop are independent events. (f) Normal distribution is right skewed. (g) Mean is more robust to outliers. So mean is used for data with extreme values. (h) It is possible to have no mode in the data. (i) Standard normal variable, Z has some unit. (j) Only two parameters are required to describe the entire normal distribution. (k) Mean of standard normal variable, Z is 1. (l) If p-value of more than level of significance (alpha), we reject the H0. (m) Very small p-value indicates rejection of H0. (n) H0 always contains equality sign. (o) CLT indicates that distribution of sample mean can be anything, not just normal. (p) Sample mean is always equal to population mean. (q) Variance of sample mean is less than population mean. (r) Variance of sample mean does not depend on sample size. (s) Mr. A has cancer but a medical doctor diagnosed him as “no cancer”. It is a type I error. (t) Level of significance is probability of making type II error. (u) Type II error can be controlled. (v) Type I error is more serious than type II error. (w) Type I and Type II errors are based on null hypothesis. Q.29 Type I and Type II Errors : Make statements about Type I (False Positive) and Type II errors (False Negative). (a) The Alpha-Fetoprotein (AFP) Test has both Type I and Type II error possibilities. This test screens the mother’s blood during pregnancy for AFP and determines risk. Abnormally high or low levels may indicate Down syndrome. (Hint: Take actual status as down syndrome or not) Ho: patient is healthy Ha: patient is unhealthy (b) The mechanic inspects the brake pads for the minimum allowable thickness. Ho: Vehicles breaks meet the standard for the minimum allowable thickness. Ha: Vehicles brakes do not meet the standard for the minimum allowable thickness. (c) Celiac disease is one of the diseases which can be misdiagnosed or have less diagnosis. Following table shows the actual celiac patients and their diagnosis status by medical doctors: Actual Status Yes No Diagnosed as celiac Yes 85 5 No 25 105 I. Calculate the probability of making type I and type II error rates. II. Calculate the power of the test. (Power of the test= 1- P(type II error) Answers: USEFUL FORMULAE: Descriptive Statistics Possible Outliers, any value beyond the range of Q 1.5( ) and Q 1.5( ) Range = Maximum value -Minimum value 100 where 1 ( ) (Preferred) 1 and , n fx x For data with repeats, 1 ( ) (Preferred ) OR 1 and n x x For data without repeats, 1 3 1 3 3 1 2 2 2 2 2 2 2 2 2 2 Q Q Q Q x s CV n f n f x x OR s n fx nx s n x x s n x nx s                             Discrete Distribution         ( ) ( ) ( ) ( ) { ( )} ( ) ( ) 2 2 2 2 E X x P X x V X E X E X E X xP X x Binomial Distribution Probability mass function, P(X=x)= x n x n x C p q  for x=0,1,2,…,n. E(X)=np, Var(X)=npq Hypothesis Testing based on Normal Distribution      X std X mean Z Standard Normal Variable, Probability Bayes Rule, ( ) ( and ) ( ) ( ) ( | ) P B P A B P B P A B P A B    Central Limit Theorem For large n (n>30), ~ ( , ) 2 n X N   and ˆ ~ ( , ) n pq p N p For hypothesis testing of μ, σ known           n x Z   For hypothesis testing of p n pq p p Z   ˆ ANSWERS: Q.1 (a) 14.286 (b) 14 (c) none (d) 10.24 (e) 22.40 Q.2 (a) 15.125 (b) 15.5 (c) No (d) 10.98 (e) 21.9 (f) English Q.3 (a) 18.6 (b)19 (c) 16, 21, and 25 (d) 15, 22 (f) slightly left (g) 7 (h) no outliers (i) increase (j) same Q.4 (a) 0.41 (b) 20 (c)14, 17, 20, 21,25 (d) 16.5, 25 (f) slightly right (g) 8.5 (h) no (i) increase (j) same Q.5 (a)56.57 (b) 22.26 (c) 8.34 Q.6 (a) 21 (b) 38.57 (c) 29.57 Q.7 (a) 410 (b) 1200 Q.8 (a)3 (b) 0.65 Q.9 (a) 0.082 (b) 0.29 (c)0.34 (d) 0.66 (e)0.10 (f) 0.64 Q.10 (a) 0.038 (b)0.23 (c) 0.71 (d) 0.29 (e)0.096 (f) 0.62 Q.11 (i)0.248 (ii)0.752 (iii)0.505 Q.12 (i)0.0875 (ii)0.913 (iii)0.425 (iii)0.488 Q.13 (a)0.22 (b)0.41 (c)0.33 (d)0.27 (e) 0.67 Q.14 (a) 0.13 (b) 0.18 (c)0.12 Q.15 E(X)=3.1 , V(X)=1.69, $0.2 per game, $ 4 win. Q.16 E(X)=5.125, V(X)=1.86, $0.25 loss per game, $5 loss. Q.17 (a)0.201 (b) 0.819, 0.027 Q.18 (a)0.9938 (b)0.0968 (c)0.452 (d)0.984 (e) 0.0433 (f)0.2353 Q.19 (a) -0.25 (b)0.71 (c) -1.13 (d)0.41 Q.20 (b) 0.7422 (c) 0.3821 (d) 0.1109 Q.21 (a)0.0014 (b) 0.0668 (c) 0.9318 Q.22 (a) 140 (b)2.37 Q.24 Z=-1.26, Accept null. Q.25 Z=-2.41, accept null Q.26 Z=4.76, reject H0 Q.27 Z=-1.75, reject H0 Q.28 F, F, F, T , F, F, F, T, F, T, F, F, T, T, F, F, T, F, T, F, F, T, T Q.29 (c)0.113 , 0.022 , 0.977 (or 98%)

Statistical Methods (STAT 4303) Review for Final Comprehensive Exam Measures of Central Tendency, Dispersion Q.1. The data below represents the test scores obtained by students in college algebra class. 10,12,15,20,13,16,14 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) Q.2. The data below represents the test scores obtained by students in English class. 12,15,16,18,13,10,17,20 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) (f) Compare the results of Q.1 and Q.2, Which scores College Algebra or English do you think is more precise (less spread)? Q.3 Following data represents the score obtained by students in one of the exams 9, 13, 14, 15, 16, 16, 17, 19, 20, 21, 21, 22, 25, 25, 26 Create a frequency table to calculate the following descriptive statistics (a) mean (b) median (c) mode (d) first and third quartiles (e) Construct Box and Whisker plot. (f) Comment on the shape of the distribution. (g) Find inter quartile range (IQR). (h) Are there any outliers (based on IQR technique)? In the above problem, if the score 26 is replaced by 37 (i) What will happen to the mean? Will it increase, decrease or remains the same? (j) What will be the new median? (k) What can you say about the effect of outliers on mean and median? Q.4 Following data represents the score obtained by students in one of the exams 19, 14, 14, 15, 17, 16, 17, 20, 20, 21, 21, 22, 25, 25, 26, 27, 28 Create a frequency table to calculate the following descriptive statistics a) mean b) median c) mode d) first and third quartiles e) Construct Box and Whisker plot. f) Comment on the shape of the distribution. g) Find inter quartile range (IQR). h) Are there any outliers (based on IQR technique)? In the above problem, if the score 28 is replaced by 48 i) What will happen to the mean? Will it increase, decrease or remains the same? j) What will be the new median? k) What can you say about the effect of outliers on mean and median? Q.5 Consider the following data of height (in inch) and weight(in lbs). Height(x) Frequency 50 2 52 3 55 2 60 4 62 3  Find the mean height.  What is the variance of height? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.6. The following table shows the number of miles run during one week for a sample of 20 runners: Miles Mid-value (x) Frequency (f) 5.5-10.5 1 10.5-15.5 2 15.5-20.5 3 20.5-25.5 5 25.5-30.5 4 (a) Find the average (mean) miles run. (Hint: Find mid-value of mile range first) (b) What is the variance of miles run? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.7. (a) If the mean of 20 observations is 20.5, find the sum of all observations? (b) If the mean of 30 observations is 40, find the sum of all observations? Probability Q.8 Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. a) How many students are in both classes? b) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? Q.9 A drawer contains 4 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and then replaced. Another ball is taken from the drawer. What is the probability that (Draw tree diagram to facilitate your calculation). (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q.10 A drawer contains 3 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and not replaced. Another ball is then taken from the drawer. Draw tree diagram to facilitate your calculation. What is the probability that (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q. 11 Missile A has 45% chance of hitting target. Missile B has 55% chance of hitting a target. What is the probability that (i) both miss the target. (ii) at least one will hit the target. (iii) exactly one will hit the target. Q. 12 A politician from D party speaks truth 65% of times; another politician from rival party speaks truth 75% of times. Both politicians were asked about their personal love affair with their own office secretary, what is the probability that (i) both lie the actual fact . (ii) at least one will speak truth. (iii) exactly one speaks the truth. (iv) both speak the truth. Q.13 The question, “Do you drink alcohol?” was asked to 220 people. Results are shown in the table. . Yes No Total Male 48 82 Female 24 66 Total (a) What is the probability of a randomly selected individual being a male also drinks? (b) What is the probability of a randomly selected individual being a female? (c) What is the probability that a randomly selected individual drinks? (d) A person is selected at random and if the person is female, what is the probability that she drinks? (e) What is the probability that a randomly selected alcoholic person is a male? Q.14 A professor, Dr. Drakula, taught courses that included statements from across the five colleges abbreviated as AH, AS, BA, ED and EN. He taught at Texas A&M University – Kingsville (TAMUK) during the span of five academic years AY09 to AY13. The following table shows the total number of graduates during AY09 to AY13. One day, he was running late to his class. He was so focused on the class that he did not stop for a red light. As soon as he crossed through the intersection, a police officer Asked him to stop. ( a ) It is turned out that the police officer was TAMUK graduate during the past five years. What is the probability that the Police Officer was from ED College? ( b ) What is the probability that the Police Officer graduated in the academic year of 2011? ( c ) If the traffic officer graduated from TAMUK in the academic year of 2011(AY11). What is the conditional probability that he graduated from the ED college? ( d ) Are the events the academic year “AY 11” and the college of Education “ED” independent? Yes or no , why? Discrete Distribution Q.15 Find k and probability for X=2 and X=4. X 1 2 3 4 5 P(X=x) 0.1 3k 0.2 2k 0.2 (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers.What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Q.16 Find k. X 3 4 5 6 7 P(X=x) k 2k 2k k 2k (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers. What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Binomial Distribution: Q.17 (a) Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover? (b) A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of (i) more than 2 hits? (ii) at least 3 misses? (c) which of the following are binomial experiments? Explain the reason. i. Telephone surveying a group of 200 people to ask if they voted for George Bush. ii. Counting the average number of dogs seen at a veterinarian’s office daily. iii. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time. iv. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.” Normal Distribution Q.18 Use standard normal distribution table to find the following probabilities: (a) P(Z<2.5) (b) P(Z< -1.3) (c) P(Z>0.12) (d) P(Z> -2.15) (e) P(0.11 ?)=0.87 (d) P(Z> ?)=0.34 Q.20. The length of life of certain type of light bulb is normally distributed with mean=220hrs and standard deviation=20hrs. (a) Define a random variable, X A light bulb is randomly selected, what is the probability that (b) it will last will last more than 207 hrs. ? (c) it will last less than 214 hrs. (d) it will last in between 199 to 207 hrs. Q.21. The length of life of an instrument produced by a machine has a normal distribution with a mean of 22 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last (a) less than 10 months. (b) more than 28 months (c) between 10 and 28 months. Distribution of sample mean and Central Limit Theorem (CLT) Q.22 It is assumed that weight of teenage student is normally distributed with mean=140 lbs. and standard deviation =15 lbs. A simple random sample of 40 teenage students is taken and sample mean is calculated. If several such samples of same size are taken (i) what could be the mean of all sample means. (ii) what could be the standard deviation of all sample means. (iii) will the distribution of sample means be normal ? (iv) What is CLT? Write down the distribution of sample mean in the form of ~ ( , ) 2 n X N   . Q.23 The time it takes students in a cooking school to learn to prepare seafood gumbo is a random variable with a normal distribution where the average is 3.2 hours and a standard deviation of 1.8 hours. A sample of 40 students was investigated. What is the distribution of sample mean (express in numbers)? Hypothesis Testing Q.24 The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203 with standard deviation of 37. Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: n=3,00, =200.3. Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring (means does the result form current examination differs from 2002 report)?? (Follow the steps below to reach the conclusion) (i) Define null and alternate hypothesis (Also write what is  , and x in words at the beginning) (ii) Identify the significance level ,  and check whether it is one sided or two sided test. (iii) Calculate test statistics, Z. (iv) Use standard normal table to find the p-value and state whether you reject or accept (fail to reject) the null hypothesis. (v) what is the critical value, do you reject or accept the H0. (vi) Write down the conclusion based on part (iv). Q.25 A sample of 145 boxes of Kellogg’s Raisin Bran contain in average 1.95 scoops of raisins. It is known from past experiments that the standard deviation for the number of scoops of raisins is 0.25. The manufacturer of Kellogg’s Raisin Bran claimed that in average their product contains more than 2 scoops of raisins, do you reject or accept the manufacturers claim (follow all five steps)? Q.26 It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg. The standard deviation from the population is 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population? Use 10% level of significance. Q.27 A CEO claims that at least 80 percent of the company’s 1,000,000 customers are very satisfied. Again, 100 customers are surveyed using simple random sampling. The result: 73 percent are very satisfied. Based on these results, should we accept or reject the CEO’s hypothesis? Assume a significance level of 0.05. Q.28 True/False questions (These questions are collected from previous HW, review and exam problems, see the previous solutions for answers) (a) Total sum of probability can exceed 1. (b) If you throw a die, getting 2 or any even number are independent events. (c) If you roll a die for 20 times, the probability of getting 5 in 15th roll is 20 15 . (d) A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. Probability that he gets the first question right is 2 1 . (e) Typing in laptop and writing emails using the same laptop are independent events. (f) Normal distribution is right skewed. (g) Mean is more robust to outliers. So mean is used for data with extreme values. (h) It is possible to have no mode in the data. (i) Standard normal variable, Z has some unit. (j) Only two parameters are required to describe the entire normal distribution. (k) Mean of standard normal variable, Z is 1. (l) If p-value of more than level of significance (alpha), we reject the H0. (m) Very small p-value indicates rejection of H0. (n) H0 always contains equality sign. (o) CLT indicates that distribution of sample mean can be anything, not just normal. (p) Sample mean is always equal to population mean. (q) Variance of sample mean is less than population mean. (r) Variance of sample mean does not depend on sample size. (s) Mr. A has cancer but a medical doctor diagnosed him as “no cancer”. It is a type I error. (t) Level of significance is probability of making type II error. (u) Type II error can be controlled. (v) Type I error is more serious than type II error. (w) Type I and Type II errors are based on null hypothesis. Q.29 Type I and Type II Errors : Make statements about Type I (False Positive) and Type II errors (False Negative). (a) The Alpha-Fetoprotein (AFP) Test has both Type I and Type II error possibilities. This test screens the mother’s blood during pregnancy for AFP and determines risk. Abnormally high or low levels may indicate Down syndrome. (Hint: Take actual status as down syndrome or not) Ho: patient is healthy Ha: patient is unhealthy (b) The mechanic inspects the brake pads for the minimum allowable thickness. Ho: Vehicles breaks meet the standard for the minimum allowable thickness. Ha: Vehicles brakes do not meet the standard for the minimum allowable thickness. (c) Celiac disease is one of the diseases which can be misdiagnosed or have less diagnosis. Following table shows the actual celiac patients and their diagnosis status by medical doctors: Actual Status Yes No Diagnosed as celiac Yes 85 5 No 25 105 I. Calculate the probability of making type I and type II error rates. II. Calculate the power of the test. (Power of the test= 1- P(type II error) Answers: USEFUL FORMULAE: Descriptive Statistics Possible Outliers, any value beyond the range of Q 1.5( ) and Q 1.5( ) Range = Maximum value -Minimum value 100 where 1 ( ) (Preferred) 1 and , n fx x For data with repeats, 1 ( ) (Preferred ) OR 1 and n x x For data without repeats, 1 3 1 3 3 1 2 2 2 2 2 2 2 2 2 2 Q Q Q Q x s CV n f n f x x OR s n fx nx s n x x s n x nx s                             Discrete Distribution         ( ) ( ) ( ) ( ) { ( )} ( ) ( ) 2 2 2 2 E X x P X x V X E X E X E X xP X x Binomial Distribution Probability mass function, P(X=x)= x n x n x C p q  for x=0,1,2,…,n. E(X)=np, Var(X)=npq Hypothesis Testing based on Normal Distribution      X std X mean Z Standard Normal Variable, Probability Bayes Rule, ( ) ( and ) ( ) ( ) ( | ) P B P A B P B P A B P A B    Central Limit Theorem For large n (n>30), ~ ( , ) 2 n X N   and ˆ ~ ( , ) n pq p N p For hypothesis testing of μ, σ known           n x Z   For hypothesis testing of p n pq p p Z   ˆ ANSWERS: Q.1 (a) 14.286 (b) 14 (c) none (d) 10.24 (e) 22.40 Q.2 (a) 15.125 (b) 15.5 (c) No (d) 10.98 (e) 21.9 (f) English Q.3 (a) 18.6 (b)19 (c) 16, 21, and 25 (d) 15, 22 (f) slightly left (g) 7 (h) no outliers (i) increase (j) same Q.4 (a) 0.41 (b) 20 (c)14, 17, 20, 21,25 (d) 16.5, 25 (f) slightly right (g) 8.5 (h) no (i) increase (j) same Q.5 (a)56.57 (b) 22.26 (c) 8.34 Q.6 (a) 21 (b) 38.57 (c) 29.57 Q.7 (a) 410 (b) 1200 Q.8 (a)3 (b) 0.65 Q.9 (a) 0.082 (b) 0.29 (c)0.34 (d) 0.66 (e)0.10 (f) 0.64 Q.10 (a) 0.038 (b)0.23 (c) 0.71 (d) 0.29 (e)0.096 (f) 0.62 Q.11 (i)0.248 (ii)0.752 (iii)0.505 Q.12 (i)0.0875 (ii)0.913 (iii)0.425 (iii)0.488 Q.13 (a)0.22 (b)0.41 (c)0.33 (d)0.27 (e) 0.67 Q.14 (a) 0.13 (b) 0.18 (c)0.12 Q.15 E(X)=3.1 , V(X)=1.69, $0.2 per game, $ 4 win. Q.16 E(X)=5.125, V(X)=1.86, $0.25 loss per game, $5 loss. Q.17 (a)0.201 (b) 0.819, 0.027 Q.18 (a)0.9938 (b)0.0968 (c)0.452 (d)0.984 (e) 0.0433 (f)0.2353 Q.19 (a) -0.25 (b)0.71 (c) -1.13 (d)0.41 Q.20 (b) 0.7422 (c) 0.3821 (d) 0.1109 Q.21 (a)0.0014 (b) 0.0668 (c) 0.9318 Q.22 (a) 140 (b)2.37 Q.24 Z=-1.26, Accept null. Q.25 Z=-2.41, accept null Q.26 Z=4.76, reject H0 Q.27 Z=-1.75, reject H0 Q.28 F, F, F, T , F, F, F, T, F, T, F, F, T, T, F, F, T, F, T, F, F, T, T Q.29 (c)0.113 , 0.022 , 0.977 (or 98%)

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PHY-102: Energy and Circular Motion Exercises Complete the following exercises. 1. A rifle with a longer barrel can fire bullets with a larger velocity than a rifle with a shorter barrel. a. Explain this using the impulse-momentum theorem. b. Explain this using the work-energy theorem 2. Use physics terms to explain the benefits of crumple zones in modern cars. 3. When a gun is fired at the shooting range, the gun recoils (moves backward). Explain this using the law of conservation of momentum. 4. Rank the following in terms of increasing inertia: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s 5. Rank the following in terms of increasing momentum: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s 6. Rank the following in terms of increasing kinetic energy: A. A 1200 kg car going 15 m/s B. A 10,000 kg train car at rest C. A 15 kg meteor going at a speed of 1000 m/s D. A 100 kg person running at 5 m/s 7. Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision. Find the speed of Ben and Junior as they move across the ice after the collision. Give the answer in m/s. Describe the work you did to get the answer. 8. Identical marbles are released from the same height on each of the following four frictionless ramps. Compare the speed of the marbles at the end of each ramp. Explain your reasoning. 9. A force of only 150 N can lift a 600 N sack of flour to a height of 0.50 m when using a lever as shown in the diagram below. a. Find the work done on the sack of flour (in J). b. Find the distance you must push with the 150 N force on the left side (in m). c. Briefly explain the benefit of using a lever to lift a heavy object. 10. Rank the following in terms of increasing power. A. Doing 100 J of work in 10 seconds. B. Doing 100 J of work in 5 seconds. C. Doing 200 J of work in 5 seconds. D. Doing 400 J of work in 30 seconds. 11. A student lifts a 25 kg mass a vertical distance of 1.6 m in a time of 2.0 seconds. a. Find the force needed to lift the mass (in N). b. Find the work done by the student (in J). c. Find the power exerted by the student (in W). 12. A satellite is put into an orbit at a distance from the center of the Earth equal to twice the distance from the center of the Earth to the surface. If the satellite had a weight at the surface of 4000 N, what is the force of gravity (weight) of the satellite when it is in its orbit? Give your answer in newtons, N. 13. Consider a satellite in a circular orbit around the Earth. a. Why is it important to give a satellite a horizontal speed when placing it in orbit? b. What will happen if the horizontal speed is too small? c. What will happen if the horizontal speed is too large? 14. If you drop an object from a distance of 1 meter above the ground, where would it fall to the ground in the shortest time: Atop Mt. Everest or in New York? 15. Why do the astronauts aboard the space station appear to be weightless? 16. Why do the passengers on a high-flying airplane not appear weightless, similar to the astronauts on the space station? 17. A ranger needs to capture a monkey hanging on a tree branch. The ranger aims his dart gun directly at the monkey and fires the tranquilizer dart. However, the monkey lets go of the branch at exactly the same time as the ranger fires the dart. Will the monkey get hit or will it avoid the dart? The remaining questions are multiple-choice questions: 18. Compared to its weight on Earth, a 5 kg object on the moon will weigh A. the same amount. B. less. C. more. 19. Compared to its mass on Earth, a 5 kg object on the moon will have A. the same mass. B. less mass. C. more mass. 20. The reason padded dashboards are used in cars is that they A. look nice and feel good. B. decrease the impulse in a collision. C. increase the force of impact in a collision. D. decrease the momentum of a collision. E. increase the time of impact in a collision. 21. Suppose you are standing on a frozen lake where there is no friction between your feet and the ice. What can you do to get off the lake? A. Bend over touching the ice in front of you and then bring you feet to your hands. B. Walk very slowly on tiptoe. C. Get on your hands and knees and crawl off the ice. D. Throw something in the direction opposite to the way you want to go. 22. A car travels in a circle with constant speed. Which of the following is true? A. The net force on the car is zero because the car is not accelerating. B. The net force on the car is directed forward, in the direction of travel. C. The net force on the car is directed inward, toward the center of the curve. D. The net force on the car is directed outward, away from the center of the curve. 23. A job is done slowly, and an identical job is done quickly. Which of the following is true? a. They require the same amount of force, but different amounts of work. b. They require the same amount of work, but different amounts of power. c. They require the same amounts of power, but different amounts of work. d. They require the same amounts of work, but different amounts of energy. 24. How many joules of work are done on a box when a force of 60 N pushes it 5 m in 3 seconds? a. 300 J b. 12 J c. 100 J d. 36 J e. 4 J 25. A 1 kg cart moving with a speed of 3 m/s collides with a 2 kg cart at rest. If the carts stick together after the collision, with what speed will they move after the collision? a. 3 m/s b. 1.5 m/s c. 1 m/s d. 2 m/s

PHY-102: Energy and Circular Motion Exercises Complete the following exercises. 1. A rifle with a longer barrel can fire bullets with a larger velocity than a rifle with a shorter barrel. a. Explain this using the impulse-momentum theorem. b. Explain this using the work-energy theorem 2. Use physics terms to explain the benefits of crumple zones in modern cars. 3. When a gun is fired at the shooting range, the gun recoils (moves backward). Explain this using the law of conservation of momentum. 4. Rank the following in terms of increasing inertia: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s 5. Rank the following in terms of increasing momentum: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s 6. Rank the following in terms of increasing kinetic energy: A. A 1200 kg car going 15 m/s B. A 10,000 kg train car at rest C. A 15 kg meteor going at a speed of 1000 m/s D. A 100 kg person running at 5 m/s 7. Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision. Find the speed of Ben and Junior as they move across the ice after the collision. Give the answer in m/s. Describe the work you did to get the answer. 8. Identical marbles are released from the same height on each of the following four frictionless ramps. Compare the speed of the marbles at the end of each ramp. Explain your reasoning. 9. A force of only 150 N can lift a 600 N sack of flour to a height of 0.50 m when using a lever as shown in the diagram below. a. Find the work done on the sack of flour (in J). b. Find the distance you must push with the 150 N force on the left side (in m). c. Briefly explain the benefit of using a lever to lift a heavy object. 10. Rank the following in terms of increasing power. A. Doing 100 J of work in 10 seconds. B. Doing 100 J of work in 5 seconds. C. Doing 200 J of work in 5 seconds. D. Doing 400 J of work in 30 seconds. 11. A student lifts a 25 kg mass a vertical distance of 1.6 m in a time of 2.0 seconds. a. Find the force needed to lift the mass (in N). b. Find the work done by the student (in J). c. Find the power exerted by the student (in W). 12. A satellite is put into an orbit at a distance from the center of the Earth equal to twice the distance from the center of the Earth to the surface. If the satellite had a weight at the surface of 4000 N, what is the force of gravity (weight) of the satellite when it is in its orbit? Give your answer in newtons, N. 13. Consider a satellite in a circular orbit around the Earth. a. Why is it important to give a satellite a horizontal speed when placing it in orbit? b. What will happen if the horizontal speed is too small? c. What will happen if the horizontal speed is too large? 14. If you drop an object from a distance of 1 meter above the ground, where would it fall to the ground in the shortest time: Atop Mt. Everest or in New York? 15. Why do the astronauts aboard the space station appear to be weightless? 16. Why do the passengers on a high-flying airplane not appear weightless, similar to the astronauts on the space station? 17. A ranger needs to capture a monkey hanging on a tree branch. The ranger aims his dart gun directly at the monkey and fires the tranquilizer dart. However, the monkey lets go of the branch at exactly the same time as the ranger fires the dart. Will the monkey get hit or will it avoid the dart? The remaining questions are multiple-choice questions: 18. Compared to its weight on Earth, a 5 kg object on the moon will weigh A. the same amount. B. less. C. more. 19. Compared to its mass on Earth, a 5 kg object on the moon will have A. the same mass. B. less mass. C. more mass. 20. The reason padded dashboards are used in cars is that they A. look nice and feel good. B. decrease the impulse in a collision. C. increase the force of impact in a collision. D. decrease the momentum of a collision. E. increase the time of impact in a collision. 21. Suppose you are standing on a frozen lake where there is no friction between your feet and the ice. What can you do to get off the lake? A. Bend over touching the ice in front of you and then bring you feet to your hands. B. Walk very slowly on tiptoe. C. Get on your hands and knees and crawl off the ice. D. Throw something in the direction opposite to the way you want to go. 22. A car travels in a circle with constant speed. Which of the following is true? A. The net force on the car is zero because the car is not accelerating. B. The net force on the car is directed forward, in the direction of travel. C. The net force on the car is directed inward, toward the center of the curve. D. The net force on the car is directed outward, away from the center of the curve. 23. A job is done slowly, and an identical job is done quickly. Which of the following is true? a. They require the same amount of force, but different amounts of work. b. They require the same amount of work, but different amounts of power. c. They require the same amounts of power, but different amounts of work. d. They require the same amounts of work, but different amounts of energy. 24. How many joules of work are done on a box when a force of 60 N pushes it 5 m in 3 seconds? a. 300 J b. 12 J c. 100 J d. 36 J e. 4 J 25. A 1 kg cart moving with a speed of 3 m/s collides with a 2 kg cart at rest. If the carts stick together after the collision, with what speed will they move after the collision? a. 3 m/s b. 1.5 m/s c. 1 m/s d. 2 m/s

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English 1 Professor Nielsen Essay One Topic and Guidelines The Context You are a non-profit organization Director of Fundraising, and your goal is to convince a wealthy individual to make a substantial donation to your cause. Choose from one of the following projects derived from the social issues from the course readings below: 1. The Prison Project: Reducing the incarceration rate and numbers in the U.S. 2. Birth Control Advocacy and Access: Supporting a birth control education and free product distribution in the U.S and/or internationally. 3. LGBT Advocacy: Funding education, campaigning, and lobbying for LGBT rights in the U.S. 4. Equality in Education: Supporting funding and scholarships for schools and individuals from less advantaged populations. 5. Migrant Welfare and Protection: Creating safe housing, food, and education for refugees. 6. Something else related to social justice?????? (See me if you have your own project idea). (animal welfare, women’s advocacy, housing, student loans and tuition affordability, etc.) Make a case for a donation of $2 million dollars to your cause by writing a funding request letter to the potential donor. This request is essentially a persuasive essay designed to convince your reader to support your cause. Below is a suggested format for organizing your letter, as well as guidelines for your work. I. The Basics Due: Tuesday, September 29, at Start of Class (Rough Draft). And Tuesday, October 6, at Start of Class (Final Draft) Length: 3-4 Pgs., double spaced in the correct format (see sample paper format template at the end of this document for format.) Font: Times New Roman, 12PT. Margins: 1 inch all around. See sample format at the end of this document for further formatting information. You are required to submit using this format. Check the sample on page five of this document carefully. Editing: Be sure to use the proofreading guide. In particular, avoid the big five errors. Revising: Read over your draft carefully several times. We will work toward revision together in class, but you will also need to revise on your own. Visit the Learning center if you need extra support. II. Organization and Content (Sample Outline Follows.) Use an organized format for your essay. The best way to ensure strong organization is to map out a plan for the content of your essay, using an outline, clustering, or other graphic representation of your key ideas. One potential format follows. Sample Method of Organizing Your Funding Letter: A. The Opening Paragraph 1. Start with some brief striking details to provide the initial background to your letter: facts, figures, brief description of one aspect of the problem- something compelling. 2. End your paragraph with a statement that briefly announces/introduces your organization without yet going into detail about your mission. State that you are requesting a donation and that your letter will describe the need for this donation. (Your Thesis) B. Body of the Letter: The Problem Make a stronger case for the problem your organization seeks to address by describing several aspects of it, using examples and details, as well as quotes from relevant class readings (be sure to cite these correctly). C. Body of the Letter: What Your Organization Will Do Describe some points of actions your group will take and ways that you will spend donor funds to address aspects of the problem you have already described. Choose three to five specific courses of action. Do not make these two extensive. They should be manageable and practical. D. Your Summary and Conclusion: Asking for Money 1. Briefly restate the problem and your organization’s goals using new wording when possible. 2. Connect the funds you need to your organization’s goals 3. Make your request for money. 4. End with a final compelling statement of why the donor should give. III. Strategies and Guidelines 1. Use the writing process steps to help you through your letter. 2. Use the proofreading guide to help you edit and the Learning Center on campus for support. 5. Cite all quotes with the author and page number. Create a works cited page at the end of your essay for the works you discuss. (See the MLA guide and sample student essays in your textbook for examples and step-by-step help with MLA. You may also pick up a guide at the campus writing center and ask them for extra help.) 6. This is NOT a research essay. Most background information should come from common knowledge, your own prior knowledge and experience, and the readings from class/the text. However, you may choose to include up one additional research source if necessary, provided this is a reliable source that you can cite correctly. Please visit OWL at Purdue University for a complete MLA citation guide. You text also has a chapter on MLA citation. 7. Follow the correct essay format for font, spacing, margins, heading, etc. (SEE sample in this document.) IV. Formatting: You are required to format your essay in the way that follows to receive full credit. • Page number in upper right-hand corner (Use “Insert” and “Pg. #”) • Times New Roman 12 Pt. font • Heading in left corner with title, student name, essay 1 (or 2, etc.), Eng 2, and date • Heading is single spaced • Skip two lines to start typing body of text • Body of text is double spaced • Margins remain at 1 inch all around. • DO NOT skip lines between paragraphs • Indent each paragraph five lines • Use MLA format for citation Continue to the next page for format sample. Title of Your Campaign Project (Choose something compelling.) Student Name Essay 1 English 1 Date Dear _______, Start typing your essay here, two lines down from heading. The body of your essay is double spaced, but the heading is only single spaced. Note the page number in the upper right-hand corner. Note the exact content of the heading. There is no title page for short essays, nor is there a title across the top. For short essays of just a few pages, this format is standard. The title goes at the top of the heading. All words in the title are capitalized except pronouns, prepositions, and articles. Do not make your margins greater that one inch. Make sure you use Times New Roman 12 Point font. Do not include graphics or images of any kind in most essays for this class (see me if you think you have an exception). When you reach the end of your paragraph, just hit return and continue typing. Do not skip lines between your paragraphs or over-indent your paragraphs; indent only five lines as marked in the ruler. Do not attempt to write less for your essay by enlarging the font, margins, or spacing. This paragraph demonstrates a good length for an introduction. You next paragraph should start here. This is the way your essay should look. You may use this template to help you format your essay by saving it to your desktop and keeping the settings. You will, of course, have two to three pages when you finish, but this is what the first page would look like roughly. If you include a quote, be sure to cite the author and page number and to include a works cited page at the end of your essay.

English 1 Professor Nielsen Essay One Topic and Guidelines The Context You are a non-profit organization Director of Fundraising, and your goal is to convince a wealthy individual to make a substantial donation to your cause. Choose from one of the following projects derived from the social issues from the course readings below: 1. The Prison Project: Reducing the incarceration rate and numbers in the U.S. 2. Birth Control Advocacy and Access: Supporting a birth control education and free product distribution in the U.S and/or internationally. 3. LGBT Advocacy: Funding education, campaigning, and lobbying for LGBT rights in the U.S. 4. Equality in Education: Supporting funding and scholarships for schools and individuals from less advantaged populations. 5. Migrant Welfare and Protection: Creating safe housing, food, and education for refugees. 6. Something else related to social justice?????? (See me if you have your own project idea). (animal welfare, women’s advocacy, housing, student loans and tuition affordability, etc.) Make a case for a donation of $2 million dollars to your cause by writing a funding request letter to the potential donor. This request is essentially a persuasive essay designed to convince your reader to support your cause. Below is a suggested format for organizing your letter, as well as guidelines for your work. I. The Basics Due: Tuesday, September 29, at Start of Class (Rough Draft). And Tuesday, October 6, at Start of Class (Final Draft) Length: 3-4 Pgs., double spaced in the correct format (see sample paper format template at the end of this document for format.) Font: Times New Roman, 12PT. Margins: 1 inch all around. See sample format at the end of this document for further formatting information. You are required to submit using this format. Check the sample on page five of this document carefully. Editing: Be sure to use the proofreading guide. In particular, avoid the big five errors. Revising: Read over your draft carefully several times. We will work toward revision together in class, but you will also need to revise on your own. Visit the Learning center if you need extra support. II. Organization and Content (Sample Outline Follows.) Use an organized format for your essay. The best way to ensure strong organization is to map out a plan for the content of your essay, using an outline, clustering, or other graphic representation of your key ideas. One potential format follows. Sample Method of Organizing Your Funding Letter: A. The Opening Paragraph 1. Start with some brief striking details to provide the initial background to your letter: facts, figures, brief description of one aspect of the problem- something compelling. 2. End your paragraph with a statement that briefly announces/introduces your organization without yet going into detail about your mission. State that you are requesting a donation and that your letter will describe the need for this donation. (Your Thesis) B. Body of the Letter: The Problem Make a stronger case for the problem your organization seeks to address by describing several aspects of it, using examples and details, as well as quotes from relevant class readings (be sure to cite these correctly). C. Body of the Letter: What Your Organization Will Do Describe some points of actions your group will take and ways that you will spend donor funds to address aspects of the problem you have already described. Choose three to five specific courses of action. Do not make these two extensive. They should be manageable and practical. D. Your Summary and Conclusion: Asking for Money 1. Briefly restate the problem and your organization’s goals using new wording when possible. 2. Connect the funds you need to your organization’s goals 3. Make your request for money. 4. End with a final compelling statement of why the donor should give. III. Strategies and Guidelines 1. Use the writing process steps to help you through your letter. 2. Use the proofreading guide to help you edit and the Learning Center on campus for support. 5. Cite all quotes with the author and page number. Create a works cited page at the end of your essay for the works you discuss. (See the MLA guide and sample student essays in your textbook for examples and step-by-step help with MLA. You may also pick up a guide at the campus writing center and ask them for extra help.) 6. This is NOT a research essay. Most background information should come from common knowledge, your own prior knowledge and experience, and the readings from class/the text. However, you may choose to include up one additional research source if necessary, provided this is a reliable source that you can cite correctly. Please visit OWL at Purdue University for a complete MLA citation guide. You text also has a chapter on MLA citation. 7. Follow the correct essay format for font, spacing, margins, heading, etc. (SEE sample in this document.) IV. Formatting: You are required to format your essay in the way that follows to receive full credit. • Page number in upper right-hand corner (Use “Insert” and “Pg. #”) • Times New Roman 12 Pt. font • Heading in left corner with title, student name, essay 1 (or 2, etc.), Eng 2, and date • Heading is single spaced • Skip two lines to start typing body of text • Body of text is double spaced • Margins remain at 1 inch all around. • DO NOT skip lines between paragraphs • Indent each paragraph five lines • Use MLA format for citation Continue to the next page for format sample. Title of Your Campaign Project (Choose something compelling.) Student Name Essay 1 English 1 Date Dear _______, Start typing your essay here, two lines down from heading. The body of your essay is double spaced, but the heading is only single spaced. Note the page number in the upper right-hand corner. Note the exact content of the heading. There is no title page for short essays, nor is there a title across the top. For short essays of just a few pages, this format is standard. The title goes at the top of the heading. All words in the title are capitalized except pronouns, prepositions, and articles. Do not make your margins greater that one inch. Make sure you use Times New Roman 12 Point font. Do not include graphics or images of any kind in most essays for this class (see me if you think you have an exception). When you reach the end of your paragraph, just hit return and continue typing. Do not skip lines between your paragraphs or over-indent your paragraphs; indent only five lines as marked in the ruler. Do not attempt to write less for your essay by enlarging the font, margins, or spacing. This paragraph demonstrates a good length for an introduction. You next paragraph should start here. This is the way your essay should look. You may use this template to help you format your essay by saving it to your desktop and keeping the settings. You will, of course, have two to three pages when you finish, but this is what the first page would look like roughly. If you include a quote, be sure to cite the author and page number and to include a works cited page at the end of your essay.

You will receive no credit for items you complete after the assignment is due. Grading Policy Exercise 2.5 Starting from the front door of your ranch house, you walk 60.0 due east to your windmill, and then you turn around and slowly walk 35.0 west to a bench where you sit and watch the sunrise. It takes you 27.0 to walk from your house to the windmill and then 49.0 to walk from the windmill to the bench. Part A For the entire trip from your front door to the bench, what is your average velocity? Express your answer with the appropriate units. ANSWER: Correct Part B For the entire trip from your front door to the bench, what is your average speed? Express your answer with the appropriate units. ANSWER: Correct Exercise 2.7 A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by , where = 2.40 and = 0.110 . = -0.329 average speed = 1.25 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 1 of 16 3/23/2015 11:12 AM Part A Calculate the average velocity of the car for the time interval = 0 to = 10.0 . ANSWER: Correct Part B Calculate the instantaneous velocity of the car at =0. ANSWER: Correct Part C Calculate the instantaneous velocity of the car at =5.00 . ANSWER: Correct Part D Calculate the instantaneous velocity of the car at =10.0 . ANSWER: Correct Part E How long after starting from rest is the car again at rest? ANSWER: = 13.0 = 0 = 15.8 = 15.0 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 2 of 16 3/23/2015 11:12 AM Correct Exercise 2.9 A ball moves in a straight line (the x-axis). The graph in the figure shows this ball’s velocity as a function of time. Part A What are the ball’s average velocity during the first 2.8 ? Express your answer using two significant figures. ANSWER: Answer Requested Part B What are the ball’s average speed during the first 2.8 ? Express your answer using two significant figures. ANSWER: Correct = 14.5 = 2.3 = 2.3 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 3 of 16 3/23/2015 11:12 AM Part C Suppose that the ball moved in such a way that the graph segment after 2.0 was -3.0 instead of +3.0 . Find the ball’s and average velocity during the first 2.8 in this case. Express your answer using two significant figures. ANSWER: All attempts used; correct answer displayed Part D Suppose that the ball moved in such a way that the graph segment after 2.0 was -3.0 instead of +3.0 . Find the ball’s average speed during the first 2.8 in this case. Express your answer using two significant figures. ANSWER: Correct Exercise 2.13 Part A The table shows test data for the Bugatti Veyron, the fastest car made. The car is moving in a straight line (the x-axis). Time 0 2.10 20.0 53.0 Speed 0 60.0 205 259 Calculate the car’s average acceleration (in ) between 0 and 2.1 . ANSWER: Correct Part B Calculate the car’s average acceleration (in ) between 2.1 and 20.0 . = 0.57 = 2.3 = 12.8 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 4 of 16 3/23/2015 11:12 AM ANSWER: Correct Part C Calculate the car’s average acceleration (in ) between 20.0 and 53 . ANSWER: Correct Exercise 2.19 An antelope moving with constant acceleration covers the distance 79.0 between two points in time 7.00 . Its speed as it passes the second point is 14.5 . Part A What is its speed at the first point? ANSWER: Correct Part B What is the acceleration? ANSWER: Correct Exercise 2.22 In the fastest measured tennis serve, the ball left the racquet at 73.14 . A served tennis ball is typically in contact with = 3.62 = 0.731 = 8.07 = 0.918 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 5 of 16 3/23/2015 11:12 AM the racquet for 27.0 and starts from rest. Assume constant acceleration. Part A What was the ball’s acceleration during this serve? ANSWER: Correct Part B How far did the ball travel during the serve? ANSWER: Correct Exercise 2.30 A cat walks in a straight line, which we shall call the x-axis with the positive direction to the right. As an observant physicist, you make measurements of this cat’s motion and construct a graph of the feline’s velocity as a function of time (the figure ). Part A Find the cat’s velocity at = 5.0 . Express your answer using two significant figures. ANSWER: = 2710 = 0.987 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 6 of 16 3/23/2015 11:12 AM Correct Part B Find the cat’s velocity at = 8.0 . Express your answer using two significant figures. ANSWER: Correct Part C What is the cat’s acceleration at ? Express your answer using two significant figures. ANSWER: Correct Part D What is the cat’s acceleration at ? Express your answer using two significant figures. ANSWER: Correct Part E What is the cat’s acceleration at ? Express your answer using two significant figures. ANSWER: = 1.3 = -2.7 = -1.3 = -1.3 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 7 of 16 3/23/2015 11:12 AM Correct Part F What distance does the cat move during the first 4.5 ? Express your answer using two significant figures. ANSWER: Correct Part G What distance does the cat move from to ? Express your answer using two significant figures. ANSWER: Correct Part H Sketch clear graph of the cat’s acceleration as function of time, assuming that the cat started at the origin. ANSWER: = -1.3 = 23 = 26 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 8 of 16 3/23/2015 11:12 AM Correct Part I Sketch clear graph of the cat’s position as function of time, assuming that the cat started at the origin. ANSWER: Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 9 of 16 3/23/2015 11:12 AM All attempts used; correct answer displayed Exercise 2.35 Part A If a flea can jump straight up to a height of 0.510 , what is its initial speed as it leaves the ground? ANSWER: Correct Part B How long is it in the air? ANSWER: Correct = 3.16 = 0.645 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 10 of 16 3/23/2015 11:12 AM Exercise 2.36 A small rock is thrown vertically upward with a speed of 18.0 from the edge of the roof of a 39.0 tall building. The rock doesn’t hit the building on its way back down and lands in the street below. Air resistance can be neglected. Part A What is the speed of the rock just before it hits the street? Express your answer with the appropriate units. ANSWER: Correct Part B How much time elapses from when the rock is thrown until it hits the street? Express your answer with the appropriate units. ANSWER: Correct Exercise 2.38 You throw a glob of putty straight up toward the ceiling, which is 3.00 above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.70 . Part A What is the speed of the putty just before it strikes the ceiling? Express your answer with the appropriate units. ANSWER: Correct Part B = 33.0 = 5.20 = 5.94 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 11 of 16 3/23/2015 11:12 AM How much time from when it leaves your hand does it take the putty to reach the ceiling? Express your answer with the appropriate units. ANSWER: Correct Exercise 3.1 A squirrel has x- and y-coordinates ( 1.2 , 3.3 ) at time and coordinates ( 5.3 , -0.80 ) at time = 2.6 . Part A For this time interval, find the x-component of the average velocity. Express your answer using two significant figures. ANSWER: Correct Part B For this time interval, find the y-component of the average velocity. Express your answer using two significant figures. ANSWER: Correct Part C Find the magnitude of the average velocity. Express your answer using two significant figures. ANSWER: = 0.384 = 1.6 = -1.6 = 2.2 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 12 of 16 3/23/2015 11:12 AM Correct Part D Find the direction of the average velocity. Express your answer using two significant figures. ANSWER: Correct Exercise 3.3 A web page designer creates an animation in which a dot on a computer screen has a position of 4.1 2.1 4.7 . Part A Find the average velocity of the dot between and . Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Part B Find the instantaneous velocity at . Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Part C = 45 below the x-axis = 4.2,4.7 = 0,4.7 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 13 of 16 3/23/2015 11:12 AM Find the instantaneous velocity at . Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Part D Find the instantaneous velocity at . Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Exercise 3.5 A jet plane is flying at a constant altitude. At time it has components of velocity 89 , 108 . At time 32.5 the components are 165 , 37 . Part A For this time interval calculate the average acceleration. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Part B Find the magnitude of the average acceleration. Express your answer using two significant figures. ANSWER: = 4.2,4.7 = 8.4,4.7 = 2.3,-2.2 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 14 of 16 3/23/2015 11:12 AM Correct Part C Find the direction of the average acceleration (let the direction be the angle that the vector makes with the +x-axis, measured counterclockwise). ANSWER: Correct Exercise 3.4 The position of a squirrel running in a park is given by . Part A What is , the -component of the velocity of the squirrel, as function of time? ANSWER: Correct Part B What is , the y-component of the velocity of the squirrel, as function of time? ANSWER: = 3.2 = -43.1 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 15 of 16 3/23/2015 11:12 AM Correct Part C At 4.51 , how far is the squirrel from its initial position? Express your answer to three significant figures and include the appropriate units. ANSWER: All attempts used; correct answer displayed Part D At 4.51 , what is the magnitude of the squirrel’s velocity? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part E At 4.51 , what is the direction (in degrees counterclockwise from +x-axis) of the squirrel’s velocity? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 90.1%. You received 14.42 out of a possible total of 16 points. = 2.65 = 1.31 = 62.5 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 16 of 16 3/23/2015 11:12 AM

You will receive no credit for items you complete after the assignment is due. Grading Policy Exercise 2.5 Starting from the front door of your ranch house, you walk 60.0 due east to your windmill, and then you turn around and slowly walk 35.0 west to a bench where you sit and watch the sunrise. It takes you 27.0 to walk from your house to the windmill and then 49.0 to walk from the windmill to the bench. Part A For the entire trip from your front door to the bench, what is your average velocity? Express your answer with the appropriate units. ANSWER: Correct Part B For the entire trip from your front door to the bench, what is your average speed? Express your answer with the appropriate units. ANSWER: Correct Exercise 2.7 A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by , where = 2.40 and = 0.110 . = -0.329 average speed = 1.25 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 1 of 16 3/23/2015 11:12 AM Part A Calculate the average velocity of the car for the time interval = 0 to = 10.0 . ANSWER: Correct Part B Calculate the instantaneous velocity of the car at =0. ANSWER: Correct Part C Calculate the instantaneous velocity of the car at =5.00 . ANSWER: Correct Part D Calculate the instantaneous velocity of the car at =10.0 . ANSWER: Correct Part E How long after starting from rest is the car again at rest? ANSWER: = 13.0 = 0 = 15.8 = 15.0 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 2 of 16 3/23/2015 11:12 AM Correct Exercise 2.9 A ball moves in a straight line (the x-axis). The graph in the figure shows this ball’s velocity as a function of time. Part A What are the ball’s average velocity during the first 2.8 ? Express your answer using two significant figures. ANSWER: Answer Requested Part B What are the ball’s average speed during the first 2.8 ? Express your answer using two significant figures. ANSWER: Correct = 14.5 = 2.3 = 2.3 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 3 of 16 3/23/2015 11:12 AM Part C Suppose that the ball moved in such a way that the graph segment after 2.0 was -3.0 instead of +3.0 . Find the ball’s and average velocity during the first 2.8 in this case. Express your answer using two significant figures. ANSWER: All attempts used; correct answer displayed Part D Suppose that the ball moved in such a way that the graph segment after 2.0 was -3.0 instead of +3.0 . Find the ball’s average speed during the first 2.8 in this case. Express your answer using two significant figures. ANSWER: Correct Exercise 2.13 Part A The table shows test data for the Bugatti Veyron, the fastest car made. The car is moving in a straight line (the x-axis). Time 0 2.10 20.0 53.0 Speed 0 60.0 205 259 Calculate the car’s average acceleration (in ) between 0 and 2.1 . ANSWER: Correct Part B Calculate the car’s average acceleration (in ) between 2.1 and 20.0 . = 0.57 = 2.3 = 12.8 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 4 of 16 3/23/2015 11:12 AM ANSWER: Correct Part C Calculate the car’s average acceleration (in ) between 20.0 and 53 . ANSWER: Correct Exercise 2.19 An antelope moving with constant acceleration covers the distance 79.0 between two points in time 7.00 . Its speed as it passes the second point is 14.5 . Part A What is its speed at the first point? ANSWER: Correct Part B What is the acceleration? ANSWER: Correct Exercise 2.22 In the fastest measured tennis serve, the ball left the racquet at 73.14 . A served tennis ball is typically in contact with = 3.62 = 0.731 = 8.07 = 0.918 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 5 of 16 3/23/2015 11:12 AM the racquet for 27.0 and starts from rest. Assume constant acceleration. Part A What was the ball’s acceleration during this serve? ANSWER: Correct Part B How far did the ball travel during the serve? ANSWER: Correct Exercise 2.30 A cat walks in a straight line, which we shall call the x-axis with the positive direction to the right. As an observant physicist, you make measurements of this cat’s motion and construct a graph of the feline’s velocity as a function of time (the figure ). Part A Find the cat’s velocity at = 5.0 . Express your answer using two significant figures. ANSWER: = 2710 = 0.987 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 6 of 16 3/23/2015 11:12 AM Correct Part B Find the cat’s velocity at = 8.0 . Express your answer using two significant figures. ANSWER: Correct Part C What is the cat’s acceleration at ? Express your answer using two significant figures. ANSWER: Correct Part D What is the cat’s acceleration at ? Express your answer using two significant figures. ANSWER: Correct Part E What is the cat’s acceleration at ? Express your answer using two significant figures. ANSWER: = 1.3 = -2.7 = -1.3 = -1.3 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 7 of 16 3/23/2015 11:12 AM Correct Part F What distance does the cat move during the first 4.5 ? Express your answer using two significant figures. ANSWER: Correct Part G What distance does the cat move from to ? Express your answer using two significant figures. ANSWER: Correct Part H Sketch clear graph of the cat’s acceleration as function of time, assuming that the cat started at the origin. ANSWER: = -1.3 = 23 = 26 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 8 of 16 3/23/2015 11:12 AM Correct Part I Sketch clear graph of the cat’s position as function of time, assuming that the cat started at the origin. ANSWER: Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 9 of 16 3/23/2015 11:12 AM All attempts used; correct answer displayed Exercise 2.35 Part A If a flea can jump straight up to a height of 0.510 , what is its initial speed as it leaves the ground? ANSWER: Correct Part B How long is it in the air? ANSWER: Correct = 3.16 = 0.645 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 10 of 16 3/23/2015 11:12 AM Exercise 2.36 A small rock is thrown vertically upward with a speed of 18.0 from the edge of the roof of a 39.0 tall building. The rock doesn’t hit the building on its way back down and lands in the street below. Air resistance can be neglected. Part A What is the speed of the rock just before it hits the street? Express your answer with the appropriate units. ANSWER: Correct Part B How much time elapses from when the rock is thrown until it hits the street? Express your answer with the appropriate units. ANSWER: Correct Exercise 2.38 You throw a glob of putty straight up toward the ceiling, which is 3.00 above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.70 . Part A What is the speed of the putty just before it strikes the ceiling? Express your answer with the appropriate units. ANSWER: Correct Part B = 33.0 = 5.20 = 5.94 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 11 of 16 3/23/2015 11:12 AM How much time from when it leaves your hand does it take the putty to reach the ceiling? Express your answer with the appropriate units. ANSWER: Correct Exercise 3.1 A squirrel has x- and y-coordinates ( 1.2 , 3.3 ) at time and coordinates ( 5.3 , -0.80 ) at time = 2.6 . Part A For this time interval, find the x-component of the average velocity. Express your answer using two significant figures. ANSWER: Correct Part B For this time interval, find the y-component of the average velocity. Express your answer using two significant figures. ANSWER: Correct Part C Find the magnitude of the average velocity. Express your answer using two significant figures. ANSWER: = 0.384 = 1.6 = -1.6 = 2.2 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 12 of 16 3/23/2015 11:12 AM Correct Part D Find the direction of the average velocity. Express your answer using two significant figures. ANSWER: Correct Exercise 3.3 A web page designer creates an animation in which a dot on a computer screen has a position of 4.1 2.1 4.7 . Part A Find the average velocity of the dot between and . Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Part B Find the instantaneous velocity at . Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Part C = 45 below the x-axis = 4.2,4.7 = 0,4.7 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 13 of 16 3/23/2015 11:12 AM Find the instantaneous velocity at . Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Part D Find the instantaneous velocity at . Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Exercise 3.5 A jet plane is flying at a constant altitude. At time it has components of velocity 89 , 108 . At time 32.5 the components are 165 , 37 . Part A For this time interval calculate the average acceleration. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures. ANSWER: Correct Part B Find the magnitude of the average acceleration. Express your answer using two significant figures. ANSWER: = 4.2,4.7 = 8.4,4.7 = 2.3,-2.2 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 14 of 16 3/23/2015 11:12 AM Correct Part C Find the direction of the average acceleration (let the direction be the angle that the vector makes with the +x-axis, measured counterclockwise). ANSWER: Correct Exercise 3.4 The position of a squirrel running in a park is given by . Part A What is , the -component of the velocity of the squirrel, as function of time? ANSWER: Correct Part B What is , the y-component of the velocity of the squirrel, as function of time? ANSWER: = 3.2 = -43.1 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 15 of 16 3/23/2015 11:12 AM Correct Part C At 4.51 , how far is the squirrel from its initial position? Express your answer to three significant figures and include the appropriate units. ANSWER: All attempts used; correct answer displayed Part D At 4.51 , what is the magnitude of the squirrel’s velocity? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part E At 4.51 , what is the direction (in degrees counterclockwise from +x-axis) of the squirrel’s velocity? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 90.1%. You received 14.42 out of a possible total of 16 points. = 2.65 = 1.31 = 62.5 Week 2 https://session.masteringphysics.com/myct/assignmentPrintView?assignme… 16 of 16 3/23/2015 11:12 AM

Phys4A: Practice problems for the 1st midterm test Fall 2015 1 If K has dimensions ML2/T 2, the k in K = kmv 2 must be: Answer: dimensionless 2. A 8.7 hour trip is made at an average speed of 73.0 km/h. If the first third of the trip (chronologically) was driven at 96.5 km/h, what was the average speed for the rest of the journey? Answer: 61 km/h 3. A car travels 95 km to the north at 70.0 km/h, then turns around and travels 21.9 km at 80.0 km/h. What is the difference between the average speed and the average velocity on this trip? Answer: 27 km/h 4. A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5s time interval. The velocity of the particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this time interval? Answer: 0.32 m/s2 5. A package is dropped from a helicopter moving upward at 15 m/s. If it takes 16.0 s before the package strikes the ground, how high above the ground was the package when it was released? (Disregard air resistance.) Answer: 1000m 6. If vector B is added to vector A, the result is 6i + j. If B is subtracted from A, the result is –4i + 7j. What is the magnitude of A? Answer: 4.1 7. Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What is the direction from the first oasis to the second oasis? Answer: 51° W of N 8 A river 1.00 mile wide flows with a constant speed of 1.00 mi/h. A man can row a boat at 2.00 mi/h. He crosses the river in a direction that puts him directly across the river from the starting point, and then he returns in a direction that puts him back at the starting point in the shortest time possible. The travel time for the man is, Answer: 1.15 h 9 An airplane is heading due east. The airspeed indicator shows that the plane is moving at a speed of 370 km/h relative to the air. If the wind is blowing from the south at 92.5 km/h, the velocity of the airplane relative to the ground is: Answer: 381 km/h at 76o east of north 10. A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the horizontal. The rock strikes the ground a horizontal distance of 25 m from the base of the building. Assume that the ground is level and that the side of the building is vertical. How tall is the building? Answer: 23.6m 11. A boy throws a rock with an initial velocity of 3.13 m/s at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory? Answer: 0.160 s 12. A helicopter is traveling at 54 m/s at a constant altitude of 100 m over a level field. If a wheel falls off the helicopter, with what speed will it hit the ground? Note: air resistance negligible. Answer: 70 m/s 13 A rescue airplane is diving at an angle of 37º below the horizontal with a speed of 250 m/s. It releases a survival package when it is at an altitude of 600 m. If air resistance is ignored, the horizontal distance of the point of impact from the plane at the moment of the package’s release is, Answer: 720 m 14. A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point. What was the angle of launch? Answer: 69.0° 15. An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m. What is the magnitude of the instantaneous acceleration of the particle during this time? Answer: 2.2 m/s2 16 A ball is whirled in a horizontal circle of radius r and speed v. The radius is increased to 2r keeping the speed of the ball constant. The period of the ball changes by a factor of Answer: two

Phys4A: Practice problems for the 1st midterm test Fall 2015 1 If K has dimensions ML2/T 2, the k in K = kmv 2 must be: Answer: dimensionless 2. A 8.7 hour trip is made at an average speed of 73.0 km/h. If the first third of the trip (chronologically) was driven at 96.5 km/h, what was the average speed for the rest of the journey? Answer: 61 km/h 3. A car travels 95 km to the north at 70.0 km/h, then turns around and travels 21.9 km at 80.0 km/h. What is the difference between the average speed and the average velocity on this trip? Answer: 27 km/h 4. A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5s time interval. The velocity of the particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this time interval? Answer: 0.32 m/s2 5. A package is dropped from a helicopter moving upward at 15 m/s. If it takes 16.0 s before the package strikes the ground, how high above the ground was the package when it was released? (Disregard air resistance.) Answer: 1000m 6. If vector B is added to vector A, the result is 6i + j. If B is subtracted from A, the result is –4i + 7j. What is the magnitude of A? Answer: 4.1 7. Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What is the direction from the first oasis to the second oasis? Answer: 51° W of N 8 A river 1.00 mile wide flows with a constant speed of 1.00 mi/h. A man can row a boat at 2.00 mi/h. He crosses the river in a direction that puts him directly across the river from the starting point, and then he returns in a direction that puts him back at the starting point in the shortest time possible. The travel time for the man is, Answer: 1.15 h 9 An airplane is heading due east. The airspeed indicator shows that the plane is moving at a speed of 370 km/h relative to the air. If the wind is blowing from the south at 92.5 km/h, the velocity of the airplane relative to the ground is: Answer: 381 km/h at 76o east of north 10. A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the horizontal. The rock strikes the ground a horizontal distance of 25 m from the base of the building. Assume that the ground is level and that the side of the building is vertical. How tall is the building? Answer: 23.6m 11. A boy throws a rock with an initial velocity of 3.13 m/s at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory? Answer: 0.160 s 12. A helicopter is traveling at 54 m/s at a constant altitude of 100 m over a level field. If a wheel falls off the helicopter, with what speed will it hit the ground? Note: air resistance negligible. Answer: 70 m/s 13 A rescue airplane is diving at an angle of 37º below the horizontal with a speed of 250 m/s. It releases a survival package when it is at an altitude of 600 m. If air resistance is ignored, the horizontal distance of the point of impact from the plane at the moment of the package’s release is, Answer: 720 m 14. A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point. What was the angle of launch? Answer: 69.0° 15. An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m. What is the magnitude of the instantaneous acceleration of the particle during this time? Answer: 2.2 m/s2 16 A ball is whirled in a horizontal circle of radius r and speed v. The radius is increased to 2r keeping the speed of the ball constant. The period of the ball changes by a factor of Answer: two

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Aristotle’s breadth of knowledge and exploration is amazing. Some of his most interesting ideas center around the ideas of happiness and virtue. What do you think about Aristotle’s suggestions for the happy life and the cultivation of virtue. Choose a virtue (e.g., courage, moderation, patience, responsibility, etc.) and also determine the excess and deficiency. Explore the meaning of this virtue and practice it through the week. As you hit the “mean” do you find yourself more happy?

Aristotle’s breadth of knowledge and exploration is amazing. Some of his most interesting ideas center around the ideas of happiness and virtue. What do you think about Aristotle’s suggestions for the happy life and the cultivation of virtue. Choose a virtue (e.g., courage, moderation, patience, responsibility, etc.) and also determine the excess and deficiency. Explore the meaning of this virtue and practice it through the week. As you hit the “mean” do you find yourself more happy?

“Happiness depends on ourselves.” additional than anyone else, Aristotle preserve … Read More...
Assignment 3 Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 2.68 As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 36.0 . Part A How fast is the watermelon going when it passes Superman? Express your answer with the appropriate units. ANSWER: Correct Problem 2.63 A motorist is driving at when she sees that a traffic light ahead has just turned red. She knows that this light stays red for , and she wants to reach the light just as it turns green again. It takes her to step on the brakes and begin slowing. Part A What is her speed as she reaches the light at the instant it turns green? Express your answer with the appropriate units. ANSWER: m/s 72.0 ms 20 m/s 200 m 15 s 1.0 s 5.71 ms Correct Conceptual Question 4.1 Part A At this instant, is the particle in the figurespeeding up, slowing down, or traveling at constant speed? ANSWER: Correct Part B Is this particle curving to the right, curving to the left, or traveling straight? Speeding up Slowing down Traveling at constant speed ANSWER: Correct Conceptual Question 4.2 Part A At this instant, is the particle in the following figure speeding up, slowing down, or traveling at constant speed? ANSWER: Curving to the right Curving to the left Traveling straight Correct Part B Is this particle curving upward, curving downward, or traveling straight? ANSWER: Correct Problem 4.8 A particle’s trajectory is described by and , where is in s. Part A What is the particle’s speed at ? ANSWER: The particle is speeding up. The particle is slowing down. The particle is traveling at constant speed. The particle is curving upward. The particle is curving downward. The particle is traveling straight. x = ( 1 −2 ) m 2 t3 t2 y = ( 1 −2t) m 2 t2 t t = 0 s v = 2 m/s Correct Part B What is the particle’s speed at ? Express your answer using two significant figures. ANSWER: Correct Part C What is the particle’s direction of motion, measured as an angle from the x-axis, at ? Express your answer using two significant figures. ANSWER: Correct Part D What is the particle’s direction of motion, measured as an angle from the x-axis, at ? Express your answer using two significant figures. ANSWER: t = 5.0s v = 18 m/s t = 0 s  = -90  counterclockwise from the +x axis. t = 5.0s  = 9.7  counterclockwise from the +x axis. Correct Problem 4.9 A rocket-powered hockey puck moves on a horizontal frictionless table. The figure shows the graph of and the figure shows the graph of , the x- and y-components of the puck’s velocity, respectively. The puck starts at the origin. Part A In which direction is the puck moving at = 3 ? Give your answer as an angle from the x-axis. Express your answer using two significant figures. ANSWER: Correct Part B vx vy t s = 51   above the x-axis How far from the origin is the puck at 5 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 4.13 A rifle is aimed horizontally at a target 51.0 away. The bullet hits the target 1.50 below the aim point. You may want to review ( pages 91 – 95) . For help with math skills, you may want to review: Quadratic Equations Part A What was the bullet’s flight time? Express your answer with the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the bullet’s trajectory, including where it leaves the gun and where it hits the target. You can assume that the gun was held parallel to the ground. Label the distances given in the problem. Choose an x-y coordinate system, making sure to label the origin. It is conventional to have x in the horizontal direction and y in the vertical direction. What is the y coordinate when the bullet leaves the gun? What is the y coordinate when it hits the target? What is the initial velocity in the y direction? What is the acceleration in the y direction? What is the equation that describes the motion in the vertical y direction as a function of time? Can you use the equation for to determine the time of flight? Why was it not necessary to include the motion in the x direction? s s = 180 cm m cm y(t) y(t) ANSWER: Correct Part B What was the bullet’s speed as it left the barrel? Express your answer with the appropriate units. Hint 1. How to approach the problem In the coordinate system introduced in Part A, what are the x coordinates when the bullet leaves the gun and when it hits the target? Is there any acceleration in the x direction? What is the equation that describes the motion in the horizontal x direction as a function of time? Can you use the equation for to determine the initial velocity? ANSWER: Correct Introduction to Projectile Motion Learning Goal: To understand the basic concepts of projectile motion. Projectile motion may seem rather complex at first. However, by breaking it down into components, you will find that it is really no different than the one-dimensional motions that you have already studied. One of the most often used techniques in physics is to divide two- and three-dimensional quantities into components. For instance, in projectile motion, a particle has some initial velocity . In general, this velocity can point in any direction on the xy plane and can have any magnitude. To make a problem more managable, it is common to break up such a quantity into its x component and its y component . 5.53×10−2 s x(t) x(t) 922 ms v vx vy Consider a particle with initial velocity that has magnitude 12.0 and is directed 60.0 above the negative x axis. Part A What is the x component of ? Express your answer in meters per second. ANSWER: Correct Part B What is the y component of ? Express your answer in meters per second. ANSWER: Correct Breaking up the velocities into components is particularly useful when the components do not affect each other. Eventually, you will learn about situations in which the components of velocity do affect one another, but for now you will only be looking at problems where they do not. So, if there is acceleration in the x direction but not in the y direction, then the x component of the velocity will change, but the y component of the velocity will not. Part C Look at this applet. The motion diagram for a projectile is displayed, as are the motion diagrams for each component. The x-component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you shined a spotlight to the left and recorded the particle’s shadow, you would get the motion diagram for its y component. How would you describe the two motion diagrams for the components? ANSWER: v m/s degrees vx v vx = -6.00 m/s vy v vy = 10.4 m/s Correct As you can see, the two components of the motion obey their own independent kinematic laws. For the vertical component, there is an acceleration downward with magnitude . Thus, you can calculate the vertical position of the particle at any time using the standard kinematic equation . Similarly, there is no acceleration in the horizontal direction, so the horizontal position of the particle is given by the standard kinematic equation . Now, consider this applet. Two balls are simultaneously dropped from a height of 5.0 . Part D How long does it take for the balls to reach the ground? Use 10 for the magnitude of the acceleration due to gravity. Express your answer in seconds to two significant figures. Hint 1. How to approach the problem The balls are released from rest at a height of 5.0 at time . Using these numbers and basic kinematics, you can determine the amount of time it takes for the balls to reach the ground. ANSWER: Correct This situation, which you have dealt with before (motion under the constant acceleration of gravity), is actually a special case of projectile motion. Think of this as projectile motion where the horizontal component of the initial velocity is zero. Both the vertical and horizontal components exhibit motion with constant nonzero acceleration. The vertical component exhibits motion with constant nonzero acceleration, whereas the horizontal component exhibits constant-velocity motion. The vertical component exhibits constant-velocity motion, whereas the horizontal component exhibits motion with constant nonzero acceleration. Both the vertical and horizontal components exhibit motion with constant velocity. g = 10 m/s2 y = y0 + v0 t + (1/2)at2 x = x0 + v0 t m tg m/s2 m t = 0 s tg = 1.0 s Part E Imagine the ball on the left is given a nonzero initial speed in the horizontal direction, while the ball on the right continues to fall with zero initial velocity. What horizontal speed must the ball on the left start with so that it hits the ground at the same position as the ball on the right? Remember that the two balls are released, starting a horizontal distance of 3.0 apart. Express your answer in meters per second to two significant figures. Hint 1. How to approach the problem Recall from Part B that the horizontal component of velocity does not change during projectile motion. Therefore, you need to find the horizontal component of velocity such that, in a time , the ball will move horizontally 3.0 . You can assume that its initial x coordinate is . ANSWER: Correct You can adjust the horizontal speeds in this applet. Notice that regardless of what horizontal speeds you give to the balls, they continue to move vertically in the same way (i.e., they are at the same y coordinate at the same time). Problem 4.12 A ball thrown horizontally at 27 travels a horizontal distance of 49 before hitting the ground. Part A From what height was the ball thrown? Express your answer using two significant figures with the appropriate units. ANSWER: vx m vx tg = 1.0 s m x0 = 0.0 m vx = 3.0 m/s m/s m h = 16 m Correct Enhanced EOC: Problem 4.20 The figure shows the angular-velocity-versus-time graph for a particle moving in a circle. You may want to review ( page ) . For help with math skills, you may want to review: The Definite Integral Part A How many revolutions does the object make during the first 3.5 ? Express your answer using two significant figures. You did not open hints for this part. ANSWER: s n = Incorrect; Try Again Problem 4.26 To withstand “g-forces” of up to 10 g’s, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a “human centrifuge.” 10 g’s is an acceleration of . Part A If the length of the centrifuge arm is 10.0 , at what speed is the rider moving when she experiences 10 g’s? Express your answer with the appropriate units. ANSWER: Correct Problem 4.28 Your roommate is working on his bicycle and has the bike upside down. He spins the 60.0 -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. Part A What is the pebble’s speed? Express your answer with the appropriate units. ANSWER: Correct 98 m/s2 m 31.3 ms cm 5.65 ms Part B What is the pebble’s acceleration? Express your answer with the appropriate units. ANSWER: Correct Enhanced EOC: Problem 4.43 On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The acceleration due to gravity on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 13 at an angle 50 above the horizontal. You may want to review ( pages 90 – 95) . For help with math skills, you may want to review: Quadratic Equations Part A How much farther did the ball travel on the moon than it would have on earth? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the path of the golf ball, showing its starting and ending points. Choose a coordinate system, and label the origin. It is conventional to let x be the horizontal direction and y the vertical direction. What is the initial velocity in the x and y directions? What is the acceleration in the x and y directions on the moon and on the earth? What are the equations for and as a function of time, and , respectively? What is the y coordinate when the golf ball hits the ground? Can you use this information to determine the time of flight on the moon and on the earth? 107 m s2 m/s  x y x(t) y(t) Once you have the time of flight, how can you use the equation to determine the total distance traveled? Compare the distance traveled on the moon to the distance traveled on the earth . ANSWER: Correct Part B For how much more time was the ball in flight? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the equation describing as a function of time? What is the initial x component of the ball’s velocity? How are the initial x component of the ball’s velocity and the distance traveled related to the time of flight? What is the difference between the time of flight on the moon and on earth? ANSWER: Correct Problem 4.42 In the Olympic shotput event, an athlete throws the shot with an initial speed of 12 at a 40.0 angle from the horizontal. The shot leaves her hand at a height of 1.8 above the ground. x(t) L = 85 m x(t) x t = 10 s m/s  m Part A How far does the shot travel? Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part B Repeat the calculation of part (a) for angles of 42.5 , 45.0 , and 47.5 . Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part C Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part D x = 16.36 m    x(42.5 ) = 16.39 m x(45.0 ) = 16.31 m Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part E At what angle of release does she throw the farthest? ANSWER: Correct Problem 4.44 A ball is thrown toward a cliff of height with a speed of 32 and an angle of 60 above horizontal. It lands on the edge of the cliff 3.2 later. Part A How high is the cliff? Express your answer to two significant figures and include the appropriate units. ANSWER: x(47.5 ) = 16.13 m 40.0 42.5 45.0 47.5 h m/s  s h = 39 m Answer Requested Part B What was the maximum height of the ball? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the ball’s impact speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 4.58 A typical laboratory centrifuge rotates at 3600 . Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. Part A What is the acceleration at the end of a test tube that is 10 from the axis of rotation? Express your answer with the appropriate units. hmax = 39 m v = 16 ms rpm cm ANSWER: Correct Part B For comparison, what is the magnitude of the acceleration a test tube would experience if dropped from a height of 1.0 and stopped in a 1.7-ms-long encounter with a hard floor? Express your answer with the appropriate units. ANSWER: Correct Problem 4.62 Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is , and the altitude of a geosynchronous orbit is ( 22000 miles). Part A What is the speed of a satellite in a geosynchronous orbit? Express your answer with the appropriate units. ANSWER: Correct a = 1.42×104 m s2 m a = 2610 m s2 6.37 × 106m 3.58 × 107m  v = 3070 ms Part B What is the magnitude of the acceleration of a satellite in a geosynchronous orbit? Express your answer with the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 89.5%. You received 103.82 out of a possible total of 116 points. a = 0.223 m s2

Assignment 3 Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 2.68 As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 36.0 . Part A How fast is the watermelon going when it passes Superman? Express your answer with the appropriate units. ANSWER: Correct Problem 2.63 A motorist is driving at when she sees that a traffic light ahead has just turned red. She knows that this light stays red for , and she wants to reach the light just as it turns green again. It takes her to step on the brakes and begin slowing. Part A What is her speed as she reaches the light at the instant it turns green? Express your answer with the appropriate units. ANSWER: m/s 72.0 ms 20 m/s 200 m 15 s 1.0 s 5.71 ms Correct Conceptual Question 4.1 Part A At this instant, is the particle in the figurespeeding up, slowing down, or traveling at constant speed? ANSWER: Correct Part B Is this particle curving to the right, curving to the left, or traveling straight? Speeding up Slowing down Traveling at constant speed ANSWER: Correct Conceptual Question 4.2 Part A At this instant, is the particle in the following figure speeding up, slowing down, or traveling at constant speed? ANSWER: Curving to the right Curving to the left Traveling straight Correct Part B Is this particle curving upward, curving downward, or traveling straight? ANSWER: Correct Problem 4.8 A particle’s trajectory is described by and , where is in s. Part A What is the particle’s speed at ? ANSWER: The particle is speeding up. The particle is slowing down. The particle is traveling at constant speed. The particle is curving upward. The particle is curving downward. The particle is traveling straight. x = ( 1 −2 ) m 2 t3 t2 y = ( 1 −2t) m 2 t2 t t = 0 s v = 2 m/s Correct Part B What is the particle’s speed at ? Express your answer using two significant figures. ANSWER: Correct Part C What is the particle’s direction of motion, measured as an angle from the x-axis, at ? Express your answer using two significant figures. ANSWER: Correct Part D What is the particle’s direction of motion, measured as an angle from the x-axis, at ? Express your answer using two significant figures. ANSWER: t = 5.0s v = 18 m/s t = 0 s  = -90  counterclockwise from the +x axis. t = 5.0s  = 9.7  counterclockwise from the +x axis. Correct Problem 4.9 A rocket-powered hockey puck moves on a horizontal frictionless table. The figure shows the graph of and the figure shows the graph of , the x- and y-components of the puck’s velocity, respectively. The puck starts at the origin. Part A In which direction is the puck moving at = 3 ? Give your answer as an angle from the x-axis. Express your answer using two significant figures. ANSWER: Correct Part B vx vy t s = 51   above the x-axis How far from the origin is the puck at 5 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 4.13 A rifle is aimed horizontally at a target 51.0 away. The bullet hits the target 1.50 below the aim point. You may want to review ( pages 91 – 95) . For help with math skills, you may want to review: Quadratic Equations Part A What was the bullet’s flight time? Express your answer with the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the bullet’s trajectory, including where it leaves the gun and where it hits the target. You can assume that the gun was held parallel to the ground. Label the distances given in the problem. Choose an x-y coordinate system, making sure to label the origin. It is conventional to have x in the horizontal direction and y in the vertical direction. What is the y coordinate when the bullet leaves the gun? What is the y coordinate when it hits the target? What is the initial velocity in the y direction? What is the acceleration in the y direction? What is the equation that describes the motion in the vertical y direction as a function of time? Can you use the equation for to determine the time of flight? Why was it not necessary to include the motion in the x direction? s s = 180 cm m cm y(t) y(t) ANSWER: Correct Part B What was the bullet’s speed as it left the barrel? Express your answer with the appropriate units. Hint 1. How to approach the problem In the coordinate system introduced in Part A, what are the x coordinates when the bullet leaves the gun and when it hits the target? Is there any acceleration in the x direction? What is the equation that describes the motion in the horizontal x direction as a function of time? Can you use the equation for to determine the initial velocity? ANSWER: Correct Introduction to Projectile Motion Learning Goal: To understand the basic concepts of projectile motion. Projectile motion may seem rather complex at first. However, by breaking it down into components, you will find that it is really no different than the one-dimensional motions that you have already studied. One of the most often used techniques in physics is to divide two- and three-dimensional quantities into components. For instance, in projectile motion, a particle has some initial velocity . In general, this velocity can point in any direction on the xy plane and can have any magnitude. To make a problem more managable, it is common to break up such a quantity into its x component and its y component . 5.53×10−2 s x(t) x(t) 922 ms v vx vy Consider a particle with initial velocity that has magnitude 12.0 and is directed 60.0 above the negative x axis. Part A What is the x component of ? Express your answer in meters per second. ANSWER: Correct Part B What is the y component of ? Express your answer in meters per second. ANSWER: Correct Breaking up the velocities into components is particularly useful when the components do not affect each other. Eventually, you will learn about situations in which the components of velocity do affect one another, but for now you will only be looking at problems where they do not. So, if there is acceleration in the x direction but not in the y direction, then the x component of the velocity will change, but the y component of the velocity will not. Part C Look at this applet. The motion diagram for a projectile is displayed, as are the motion diagrams for each component. The x-component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you shined a spotlight to the left and recorded the particle’s shadow, you would get the motion diagram for its y component. How would you describe the two motion diagrams for the components? ANSWER: v m/s degrees vx v vx = -6.00 m/s vy v vy = 10.4 m/s Correct As you can see, the two components of the motion obey their own independent kinematic laws. For the vertical component, there is an acceleration downward with magnitude . Thus, you can calculate the vertical position of the particle at any time using the standard kinematic equation . Similarly, there is no acceleration in the horizontal direction, so the horizontal position of the particle is given by the standard kinematic equation . Now, consider this applet. Two balls are simultaneously dropped from a height of 5.0 . Part D How long does it take for the balls to reach the ground? Use 10 for the magnitude of the acceleration due to gravity. Express your answer in seconds to two significant figures. Hint 1. How to approach the problem The balls are released from rest at a height of 5.0 at time . Using these numbers and basic kinematics, you can determine the amount of time it takes for the balls to reach the ground. ANSWER: Correct This situation, which you have dealt with before (motion under the constant acceleration of gravity), is actually a special case of projectile motion. Think of this as projectile motion where the horizontal component of the initial velocity is zero. Both the vertical and horizontal components exhibit motion with constant nonzero acceleration. The vertical component exhibits motion with constant nonzero acceleration, whereas the horizontal component exhibits constant-velocity motion. The vertical component exhibits constant-velocity motion, whereas the horizontal component exhibits motion with constant nonzero acceleration. Both the vertical and horizontal components exhibit motion with constant velocity. g = 10 m/s2 y = y0 + v0 t + (1/2)at2 x = x0 + v0 t m tg m/s2 m t = 0 s tg = 1.0 s Part E Imagine the ball on the left is given a nonzero initial speed in the horizontal direction, while the ball on the right continues to fall with zero initial velocity. What horizontal speed must the ball on the left start with so that it hits the ground at the same position as the ball on the right? Remember that the two balls are released, starting a horizontal distance of 3.0 apart. Express your answer in meters per second to two significant figures. Hint 1. How to approach the problem Recall from Part B that the horizontal component of velocity does not change during projectile motion. Therefore, you need to find the horizontal component of velocity such that, in a time , the ball will move horizontally 3.0 . You can assume that its initial x coordinate is . ANSWER: Correct You can adjust the horizontal speeds in this applet. Notice that regardless of what horizontal speeds you give to the balls, they continue to move vertically in the same way (i.e., they are at the same y coordinate at the same time). Problem 4.12 A ball thrown horizontally at 27 travels a horizontal distance of 49 before hitting the ground. Part A From what height was the ball thrown? Express your answer using two significant figures with the appropriate units. ANSWER: vx m vx tg = 1.0 s m x0 = 0.0 m vx = 3.0 m/s m/s m h = 16 m Correct Enhanced EOC: Problem 4.20 The figure shows the angular-velocity-versus-time graph for a particle moving in a circle. You may want to review ( page ) . For help with math skills, you may want to review: The Definite Integral Part A How many revolutions does the object make during the first 3.5 ? Express your answer using two significant figures. You did not open hints for this part. ANSWER: s n = Incorrect; Try Again Problem 4.26 To withstand “g-forces” of up to 10 g’s, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a “human centrifuge.” 10 g’s is an acceleration of . Part A If the length of the centrifuge arm is 10.0 , at what speed is the rider moving when she experiences 10 g’s? Express your answer with the appropriate units. ANSWER: Correct Problem 4.28 Your roommate is working on his bicycle and has the bike upside down. He spins the 60.0 -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. Part A What is the pebble’s speed? Express your answer with the appropriate units. ANSWER: Correct 98 m/s2 m 31.3 ms cm 5.65 ms Part B What is the pebble’s acceleration? Express your answer with the appropriate units. ANSWER: Correct Enhanced EOC: Problem 4.43 On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The acceleration due to gravity on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 13 at an angle 50 above the horizontal. You may want to review ( pages 90 – 95) . For help with math skills, you may want to review: Quadratic Equations Part A How much farther did the ball travel on the moon than it would have on earth? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the path of the golf ball, showing its starting and ending points. Choose a coordinate system, and label the origin. It is conventional to let x be the horizontal direction and y the vertical direction. What is the initial velocity in the x and y directions? What is the acceleration in the x and y directions on the moon and on the earth? What are the equations for and as a function of time, and , respectively? What is the y coordinate when the golf ball hits the ground? Can you use this information to determine the time of flight on the moon and on the earth? 107 m s2 m/s  x y x(t) y(t) Once you have the time of flight, how can you use the equation to determine the total distance traveled? Compare the distance traveled on the moon to the distance traveled on the earth . ANSWER: Correct Part B For how much more time was the ball in flight? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the equation describing as a function of time? What is the initial x component of the ball’s velocity? How are the initial x component of the ball’s velocity and the distance traveled related to the time of flight? What is the difference between the time of flight on the moon and on earth? ANSWER: Correct Problem 4.42 In the Olympic shotput event, an athlete throws the shot with an initial speed of 12 at a 40.0 angle from the horizontal. The shot leaves her hand at a height of 1.8 above the ground. x(t) L = 85 m x(t) x t = 10 s m/s  m Part A How far does the shot travel? Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part B Repeat the calculation of part (a) for angles of 42.5 , 45.0 , and 47.5 . Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part C Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part D x = 16.36 m    x(42.5 ) = 16.39 m x(45.0 ) = 16.31 m Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part E At what angle of release does she throw the farthest? ANSWER: Correct Problem 4.44 A ball is thrown toward a cliff of height with a speed of 32 and an angle of 60 above horizontal. It lands on the edge of the cliff 3.2 later. Part A How high is the cliff? Express your answer to two significant figures and include the appropriate units. ANSWER: x(47.5 ) = 16.13 m 40.0 42.5 45.0 47.5 h m/s  s h = 39 m Answer Requested Part B What was the maximum height of the ball? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the ball’s impact speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 4.58 A typical laboratory centrifuge rotates at 3600 . Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. Part A What is the acceleration at the end of a test tube that is 10 from the axis of rotation? Express your answer with the appropriate units. hmax = 39 m v = 16 ms rpm cm ANSWER: Correct Part B For comparison, what is the magnitude of the acceleration a test tube would experience if dropped from a height of 1.0 and stopped in a 1.7-ms-long encounter with a hard floor? Express your answer with the appropriate units. ANSWER: Correct Problem 4.62 Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is , and the altitude of a geosynchronous orbit is ( 22000 miles). Part A What is the speed of a satellite in a geosynchronous orbit? Express your answer with the appropriate units. ANSWER: Correct a = 1.42×104 m s2 m a = 2610 m s2 6.37 × 106m 3.58 × 107m  v = 3070 ms Part B What is the magnitude of the acceleration of a satellite in a geosynchronous orbit? Express your answer with the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 89.5%. You received 103.82 out of a possible total of 116 points. a = 0.223 m s2

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