Scenario: You are to design synchronous and asynchronous circuits that will allow the following requirements to be met. Tasks: 1. Packet number checking A synchronous sequential machine is to have a single input line and a single output line. The circuit is to receive messages of 4-bit words coded in binary (least significant bit first). The purpose of the circuit is to detect whether the number coming in is a prime number (divisible by only itself and 1). Thus, the output is to become 1 whenever a 4-bit word does represent a valid prime number. At the end of each word the machine is to return to the reset starting state. Steps: 1) Draw a State Diagram (Mealy) and check for redundancies 2) Then assign binary State Identifiers. 3) Make a Next State Truth Table (NSTT) 4) Select a bistable type 5) Determine expressions for the bistable inputs 6) Determine expressions for the outputs 2. Monitoring System A monitoring system sends 1s positive going pulses to a device to ensure that it is operating correctly. The device will respond by lowering its normally high line as soon as it receives the pulse then raising the line again within the 1s if working correctly. If the device line doesn’t respond correctly or respond at all then an alarm must occur. 1) Carry out a design for the asynchronous system that will realise the requirements up to the point where internal conditions are designated to the lines in the merged table. 2) Explain what the designer would have to do to ensure the system was hazard free and the output was as short as possible.

Scenario: You are to design synchronous and asynchronous circuits that will allow the following requirements to be met. Tasks: 1. Packet number checking A synchronous sequential machine is to have a single input line and a single output line. The circuit is to receive messages of 4-bit words coded in binary (least significant bit first). The purpose of the circuit is to detect whether the number coming in is a prime number (divisible by only itself and 1). Thus, the output is to become 1 whenever a 4-bit word does represent a valid prime number. At the end of each word the machine is to return to the reset starting state. Steps: 1) Draw a State Diagram (Mealy) and check for redundancies 2) Then assign binary State Identifiers. 3) Make a Next State Truth Table (NSTT) 4) Select a bistable type 5) Determine expressions for the bistable inputs 6) Determine expressions for the outputs 2. Monitoring System A monitoring system sends 1s positive going pulses to a device to ensure that it is operating correctly. The device will respond by lowering its normally high line as soon as it receives the pulse then raising the line again within the 1s if working correctly. If the device line doesn’t respond correctly or respond at all then an alarm must occur. 1) Carry out a design for the asynchronous system that will realise the requirements up to the point where internal conditions are designated to the lines in the merged table. 2) Explain what the designer would have to do to ensure the system was hazard free and the output was as short as possible.

Scenario: You are to design synchronous and asynchronous circuits that … Read More...
The current recommendation for most women, after becoming sexually active or starting at age 21, is to have a Pap smear done Question 9 options: once every year once every 6 months once every 3 years once every 5 years

The current recommendation for most women, after becoming sexually active or starting at age 21, is to have a Pap smear done Question 9 options: once every year once every 6 months once every 3 years once every 5 years

2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm on Saturday, February 28, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A Which two vectors, when added, will have the largest (positive) x component? You did not open hints for this part. ANSWER: Part B Which two vectors, when added, will have the largest (positive) y component? You did not open hints for this part. ANSWER: C and E E and F A and F C and D B and D 2/24/2015 Assignment 2 =3484333 2/22 Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? You did not open hints for this part. ANSWER: Components of Vectors Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from 5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. Part A C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F _._ _._ ._ 2/24/2015 Assignment 2 =3484333 3/22 What is the x component of ? Express your answer to two significant figures. You did not open hints for this part. ANSWER: Part B What is the y component of ? Express your answer to the nearest integer. ANSWER: Part C What is the y component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: Part D What is the component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: _._ _4 = _._ _5 = _._ _5 = 4 _._ _4 = 2/24/2015 Assignment 2 =3484333 4/22 The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation. The answers below are all integers, so estimate the components to the nearest whole number. Part E In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part F In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part G What is true about and ? Choose from the pulldown list below. ANSWER: Finding the Cross Product The figure shows two vectors and separated by an angle . You are given that , , and . _._ _._ _4, _5 = _._ _4 , _5 = _._ _._ They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors. _ ._ _._ J56 _ .__ _ _ _ _.__ _ _ _ _ ._g_.__ _ ._ 2/24/2015 Assignment 2 =3484333 5/22 Part A Express as an ordered triplet of values, separated by commas. ANSWER: Part B Find the magnitude of . ANSWER: Part C Find the sine of the angle between and . ANSWER: Significant Figures Conceptual Question In the parts that follow select whether the number presented in statement A is greater than, less than, or equal to the number presented in statement B. Be sure to follow all of the rules concerning significant figures. _ ._ _ ._= _ ._ ]_ ]._ = _ ._ _._ TJO J__ = 2/24/2015 Assignment 2 =3484333 6/22 Part A Statement A: 2.567 , to two significant figures. Statement B: 2.567 , to three significant figures. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: Part B Statement A: (2.567 + 3.146 ), to two significant figures. Statement B: (2.567 , to two significant figures) + (3.146 , to two significant figures). Determine the correct relationship between the statements. ANSWER: Part C Statement A: Area of a rectangle with measured length = 2.536 and width = 1.4 . Statement B: Area of a rectangle with measured length = 2.536 and width = 1.41 . Since you are not told specific numbers of significant figures to round to, you must use the rules for multiplying numbers while respecting significant figures. If you need a reminder, consult the hint. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: LN LN Statement A is greater than less than equal to Statement B. LN LN LN LN Statement A is greater than less than equal to Statement B. N N N N 2/24/2015 Assignment 2 =3484333 7/22 ± Vector Dot Product Let vectors , , and . Calculate the following: Part A You did not open hints for this part. ANSWER: Part B What is the angle between and ? Express your answer using one significant figure. You did not open hints for this part. ANSWER: Part C ANSWER: Part D ANSWER: Statement A is greater than less than equal to Statement B. _.__ _ _Ã_ _.__ Ã_ _ _ _.__ Ã_Ã_ _ _._ø _._ = J”# _._ _._ J”# = SBEJBOT __._ø __._ = 2/24/2015 Assignment 2 =3484333 8/22 Part E Which of the following can be computed? You did not open hints for this part. ANSWER: and are different vectors with lengths and respectively. Find the following: Part F Express your answer in terms of You did not open hints for this part. ANSWER: Part G If and are perpendicular, You did not open hints for this part. ANSWER: _ _._ø __._ = _._ø _._ø _._ _._ø _._ø _._ _._ø _.___._ _ ø _._ _ .__ _ .__ __ __ __ = ø _ .__ _ .__ _ .__ _ .__ = ø _ .__ _ .__ 2/24/2015 Assignment 2 =3484333 9/22 Part H If and are parallel, Express your answer in terms of and . You did not open hints for this part. ANSWER: ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Part A Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part B _ .__ _ .__ __ __ = ø _ .__ _ .__ _ ._ _ È _._ _ C È _._ = ._ 2/24/2015 Assignment 2 =3484333 10/22 Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part C Find the components of the vector with length = 1.00 and angle 30.0 as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Exercise 1.28 Part A How many dollar bills would you have to stack to reach the moon? (Depending on age, dollar bills can be stacked with about 23 per millimeter.) Express your answer using one significant figure. ANSWER: Problem 1.80 A boulder of weight rests on a hillside that rises at a constant angle above the horizontal, as shown in the figure . Its weight is a force on the boulder that has direction vertically downward. _._ _ D È _._ = _._ _ ] _ È _._ = dollar bills 3 C 2/24/2015 Assignment 2 =3484333 11/22 Part A In terms of and , what is the component of the weight of the boulder in the direction parallel to the surface of the hill? Express your answer in terms of and . ANSWER: Part B What is the component of the weight in the direction perpendicular to the surface of the hill? Express your answer in terms of and . ANSWER: Part C An air conditioner unit is fastened to a roof that slopes upward at an angle of . In order that the unit not slide down the roof, the component of the unit’s weight parallel to the roof cannot exceed 550 N. What is the maximum allowed weight of the unit? ANSWER: Problem 1.84 You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 23.5 from yours, in the direction 19.0 north of east. Karl’s tent is 40.0 from yours, in the direction 36.0 south of east. C 3 C 3 ]3,_. ] = C 3 ]3,!., ] = ____È 3 = / N È N È 2/24/2015 Assignment 2 =3484333 12/22 Part A What is the distance between Karl’s tent and Joe’s tent? ANSWER: Multiple Choice Question 1.8 Part A The components of vectors and are given as follows: Ax = +5.7 Bx = 9.8 Ay = 3.6 By = 6.5 The magnitude of the vector difference , is closest to: ANSWER: OneDimensional Kinematics with Constant Acceleration Learning Goal: To understand the meaning of the variables that appear in the equations for onedimensional kinematics with constant acceleration. Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or thrown) objects and cars starting and stopping approximate this type of motion. It is also the type of motion most frequently involved in introductory kinematics problems. The kinematic equations for such motion can be written as , , where the symbols are defined as follows: is the position of the particle; _ = N _ ¥ _ ¥ à _ ¥ _ ¥ 5.0 11 5.0 16 250 4 0_ 4J_2J0_ _ __ 0_ 2 0 _ 2J __0 4 0 2/24/2015 Assignment 2 =3484333 13/22 is the initial position of the particle; is the velocity of the particle; is the initial velocity of the particle; is the acceleration of the particle. In anwering the following questions, assume that the acceleration is constant and nonzero: . Part A The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part B The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part C The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part D The quantity represented by is a function of time (i.e., is not constant). ANSWER: 4J 2 0 2J _ _ Ü _ 4 true false 4J true false 2J true false 2 true false 2/24/2015 Assignment 2 =3484333 14/22 Part E Which of the given equations is not an explicit function of and is therefore useful when you don’t know or don’t need the time? ANSWER: Part F A particle moves with constant acceleration . The expression represents the particle’s velocity at what instant in time? ANSWER: More generally, the equations of motion can be written as and . Here is the time that has elapsed since the beginning of the particle’s motion, that is, , where is the current time and is the time at which we start measuring the particle’s motion. The terms and are, respectively, the position and velocity at . As you can now see, the equations given at the beginning of this problem correspond to the case , which is a convenient choice if there is only one particle of interest. To illustrate the use of these more general equations, consider the motion of two particles, A and B. The position of particle A depends on time as . That is, particle A starts moving at time with velocity , from . At time , particle B has twice the acceleration, half the velocity, and the same position that particle A had at time . Part G What is the equation describing the position of particle B? You did not open hints for this part. ANSWER: 0 4_ 4J_2J0_ _ __ 0_ 2 _ 2J __0 _ ___ 4à 2_ 2_J 4J _ 2J __0 only at time only at the “initial” time when a time has passed since the particle’s velocity was 0 _ _ 0 2J 4 0_ 4J_2J 0_ _ 0 __ _ 2 0 _ 2J __ 0 0 0 _ 0Ã0J 0 0J 4J 2J 0 _ 0J 0J _ _ 4″ 0 _ 4J _2J0_ ____0_ 0 _ 0J” _ _ 2J” _ 2J 4J” _ 4J 0 _ 0_ 0 _ _ 2/24/2015 Assignment 2 =3484333 15/22 Part H At what time does the velocity of particle B equal that of particle A? You did not open hints for this part. ANSWER: Given Positions, Find Velocity and Acceleration Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time. The table shows the x coordinate of a moving object. The position is tabulated at 1s intervals. The x coordinate is indicated below each time. You should make the simplification that the acceleration of the object is bounded and contains no spikes. time (s) 0 1 2 3 4 5 6 7 8 9 x (m) 0 1 4 9 16 24 32 40 46 48 Part A Which graph best represents the function , describing the object’s position vs. time? 4# 0_ 4J__2J0_ _ __ 0_ 4# 0 _ 4J ____2J0__0_ 4# 0_ 4J__2J 0_0__ _ 0_ __ 0__ 4# 0 _ 4J ____2J 0_0_ __ 0_0_ _ 4# 0_ 4J__2J 0Ã0__ _ 0à __ 0__ 4# 0 _ 4J ____2J 0Ã0_ __ 0Ã0_ _ The two particles never have the same velocity. 0_ 0__ 2J __ 0__0__ 2J __ 0__0__ 2J __ 4 0 2/24/2015 Assignment 2 =3484333 16/22 You did not open hints for this part. ANSWER: Part B Which of the following graphs best represents the function , describing the object’s velocity as a function of time? You did not open hints for this part. ANSWER: 1 2 3 4 2 0 2/24/2015 Assignment 2 =3484333 17/22 Part C Which of the following graphs best represents the function , describing the acceleration of this object? You did not open hints for this part. ANSWER: A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. 1 2 3 4 _ 0 1 2 3 4 _ 0 _ _ _ _ 4 _ _ 2/24/2015 Assignment 2 =3484333 18/22 Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . You did not open hints for this part. ANSWER: Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . You did not open hints for this part. ANSWER: Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . You did not open hints for this part. 4NBO 0 _ _ 0 4NBO 0 = 4CVT 0 _ 0 4CVT = 0DBUDI 2/24/2015 Assignment 2 =3484333 19/22 ANSWER: Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Stopping on Snow Light, dry snow is called powder. Skiing on a powder day is different than skiing on a day when the snow is wet and heavy. When you slow down on dry snow the maximum (negative) acceleration caused by the snow acting on your skis is about twofifths as much as that of stopping on wet snow. Part A For a given initial velocity, how does the time it takes to stop on dry snow differ from the time it takes to stop on wet snow? You did not open hints for this part. ANSWER: Part B For a given initial velocity, how does the stopping distance on dry snow differ from the stopping distance on wet snow? 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI _ _ _ Ç 0DBUDI 0E 0X 0E _ ___0X 0E _ 0X 0E _ ___0X 4E 4X 2/24/2015 Assignment 2 =3484333 20/22 You did not open hints for this part. ANSWER: Exercise 2.34 A subway train starts from rest at a station and accelerates at a rate of for 14.0 . It runs at constant speed for 70.0 and slows down at a rate of until it stops at the next station. Part A Find the total distance covered. ANSWER: Problem 2.57 Dan gets on Interstate Highway I280 at Seward, Nebraska, and drives due west in a straight line and at an average velocity of magnitude 88.0 . After traveling 76 km, he reaches the Aurora exit . Realizing he has gone too far, he turns around and drives due east 34 back to the York exit at an average velocity of magnitude 75.0 . Part A For his whole trip from Seward to the York exit, what is his average speed? 4E _ ___4X 4E _ 4X 4E _ ___4X ____ N_T_ T T ____ N_T_ = LN LN_I LN LN_I 2/24/2015 Assignment 2 =3484333 21/22 ANSWER: Part B For his whole trip from Seward to the York exit, what is the magnitude of his average velocity? ANSWER: Multiple Choice Question 2.1 Part A A train starts from rest and accelerates uniformly, until it has traveled 5.9 km and acquired a velocity of 35 m/s. The train then moves at a constant velocity of 35 m/s for 400 s. The train then decelerates uniformly at 0.065 m/s2, until it is brought to a halt. The acceleration during the first 5.9 km of travel is closest to: ANSWER: Multiple Choice Question 2.8 Part A A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during collision? ANSWER: 2 = LN_I 2 = LN_I 0.13 m/s2 0.11 m/s2 0.12 m/s2 0.10 m/s2 0.093 m/s2 2/24/2015 Assignment 2 Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 18 points. zero 200 m/s2 1500 m/s2 1300 m/s2 2800 m/s2

2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm on Saturday, February 28, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A Which two vectors, when added, will have the largest (positive) x component? You did not open hints for this part. ANSWER: Part B Which two vectors, when added, will have the largest (positive) y component? You did not open hints for this part. ANSWER: C and E E and F A and F C and D B and D 2/24/2015 Assignment 2 =3484333 2/22 Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? You did not open hints for this part. ANSWER: Components of Vectors Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from 5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. Part A C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F _._ _._ ._ 2/24/2015 Assignment 2 =3484333 3/22 What is the x component of ? Express your answer to two significant figures. You did not open hints for this part. ANSWER: Part B What is the y component of ? Express your answer to the nearest integer. ANSWER: Part C What is the y component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: Part D What is the component of ? Express your answer to the nearest integer. You did not open hints for this part. ANSWER: _._ _4 = _._ _5 = _._ _5 = 4 _._ _4 = 2/24/2015 Assignment 2 =3484333 4/22 The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation. The answers below are all integers, so estimate the components to the nearest whole number. Part E In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part F In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Part G What is true about and ? Choose from the pulldown list below. ANSWER: Finding the Cross Product The figure shows two vectors and separated by an angle . You are given that , , and . _._ _._ _4, _5 = _._ _4 , _5 = _._ _._ They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors. _ ._ _._ J56 _ .__ _ _ _ _.__ _ _ _ _ ._g_.__ _ ._ 2/24/2015 Assignment 2 =3484333 5/22 Part A Express as an ordered triplet of values, separated by commas. ANSWER: Part B Find the magnitude of . ANSWER: Part C Find the sine of the angle between and . ANSWER: Significant Figures Conceptual Question In the parts that follow select whether the number presented in statement A is greater than, less than, or equal to the number presented in statement B. Be sure to follow all of the rules concerning significant figures. _ ._ _ ._= _ ._ ]_ ]._ = _ ._ _._ TJO J__ = 2/24/2015 Assignment 2 =3484333 6/22 Part A Statement A: 2.567 , to two significant figures. Statement B: 2.567 , to three significant figures. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: Part B Statement A: (2.567 + 3.146 ), to two significant figures. Statement B: (2.567 , to two significant figures) + (3.146 , to two significant figures). Determine the correct relationship between the statements. ANSWER: Part C Statement A: Area of a rectangle with measured length = 2.536 and width = 1.4 . Statement B: Area of a rectangle with measured length = 2.536 and width = 1.41 . Since you are not told specific numbers of significant figures to round to, you must use the rules for multiplying numbers while respecting significant figures. If you need a reminder, consult the hint. Determine the correct relationship between the statements. You did not open hints for this part. ANSWER: LN LN Statement A is greater than less than equal to Statement B. LN LN LN LN Statement A is greater than less than equal to Statement B. N N N N 2/24/2015 Assignment 2 =3484333 7/22 ± Vector Dot Product Let vectors , , and . Calculate the following: Part A You did not open hints for this part. ANSWER: Part B What is the angle between and ? Express your answer using one significant figure. You did not open hints for this part. ANSWER: Part C ANSWER: Part D ANSWER: Statement A is greater than less than equal to Statement B. _.__ _ _Ã_ _.__ Ã_ _ _ _.__ Ã_Ã_ _ _._ø _._ = J”# _._ _._ J”# = SBEJBOT __._ø __._ = 2/24/2015 Assignment 2 =3484333 8/22 Part E Which of the following can be computed? You did not open hints for this part. ANSWER: and are different vectors with lengths and respectively. Find the following: Part F Express your answer in terms of You did not open hints for this part. ANSWER: Part G If and are perpendicular, You did not open hints for this part. ANSWER: _ _._ø __._ = _._ø _._ø _._ _._ø _._ø _._ _._ø _.___._ _ ø _._ _ .__ _ .__ __ __ __ = ø _ .__ _ .__ _ .__ _ .__ = ø _ .__ _ .__ 2/24/2015 Assignment 2 =3484333 9/22 Part H If and are parallel, Express your answer in terms of and . You did not open hints for this part. ANSWER: ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Part A Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part B _ .__ _ .__ __ __ = ø _ .__ _ .__ _ ._ _ È _._ _ C È _._ = ._ 2/24/2015 Assignment 2 =3484333 10/22 Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Part C Find the components of the vector with length = 1.00 and angle 30.0 as shown. Enter the x component followed by the y component, separated by a comma. You did not open hints for this part. ANSWER: Exercise 1.28 Part A How many dollar bills would you have to stack to reach the moon? (Depending on age, dollar bills can be stacked with about 23 per millimeter.) Express your answer using one significant figure. ANSWER: Problem 1.80 A boulder of weight rests on a hillside that rises at a constant angle above the horizontal, as shown in the figure . Its weight is a force on the boulder that has direction vertically downward. _._ _ D È _._ = _._ _ ] _ È _._ = dollar bills 3 C 2/24/2015 Assignment 2 =3484333 11/22 Part A In terms of and , what is the component of the weight of the boulder in the direction parallel to the surface of the hill? Express your answer in terms of and . ANSWER: Part B What is the component of the weight in the direction perpendicular to the surface of the hill? Express your answer in terms of and . ANSWER: Part C An air conditioner unit is fastened to a roof that slopes upward at an angle of . In order that the unit not slide down the roof, the component of the unit’s weight parallel to the roof cannot exceed 550 N. What is the maximum allowed weight of the unit? ANSWER: Problem 1.84 You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 23.5 from yours, in the direction 19.0 north of east. Karl’s tent is 40.0 from yours, in the direction 36.0 south of east. C 3 C 3 ]3,_. ] = C 3 ]3,!., ] = ____È 3 = / N È N È 2/24/2015 Assignment 2 =3484333 12/22 Part A What is the distance between Karl’s tent and Joe’s tent? ANSWER: Multiple Choice Question 1.8 Part A The components of vectors and are given as follows: Ax = +5.7 Bx = 9.8 Ay = 3.6 By = 6.5 The magnitude of the vector difference , is closest to: ANSWER: OneDimensional Kinematics with Constant Acceleration Learning Goal: To understand the meaning of the variables that appear in the equations for onedimensional kinematics with constant acceleration. Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or thrown) objects and cars starting and stopping approximate this type of motion. It is also the type of motion most frequently involved in introductory kinematics problems. The kinematic equations for such motion can be written as , , where the symbols are defined as follows: is the position of the particle; _ = N _ ¥ _ ¥ à _ ¥ _ ¥ 5.0 11 5.0 16 250 4 0_ 4J_2J0_ _ __ 0_ 2 0 _ 2J __0 4 0 2/24/2015 Assignment 2 =3484333 13/22 is the initial position of the particle; is the velocity of the particle; is the initial velocity of the particle; is the acceleration of the particle. In anwering the following questions, assume that the acceleration is constant and nonzero: . Part A The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part B The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part C The quantity represented by is a function of time (i.e., is not constant). ANSWER: Part D The quantity represented by is a function of time (i.e., is not constant). ANSWER: 4J 2 0 2J _ _ Ü _ 4 true false 4J true false 2J true false 2 true false 2/24/2015 Assignment 2 =3484333 14/22 Part E Which of the given equations is not an explicit function of and is therefore useful when you don’t know or don’t need the time? ANSWER: Part F A particle moves with constant acceleration . The expression represents the particle’s velocity at what instant in time? ANSWER: More generally, the equations of motion can be written as and . Here is the time that has elapsed since the beginning of the particle’s motion, that is, , where is the current time and is the time at which we start measuring the particle’s motion. The terms and are, respectively, the position and velocity at . As you can now see, the equations given at the beginning of this problem correspond to the case , which is a convenient choice if there is only one particle of interest. To illustrate the use of these more general equations, consider the motion of two particles, A and B. The position of particle A depends on time as . That is, particle A starts moving at time with velocity , from . At time , particle B has twice the acceleration, half the velocity, and the same position that particle A had at time . Part G What is the equation describing the position of particle B? You did not open hints for this part. ANSWER: 0 4_ 4J_2J0_ _ __ 0_ 2 _ 2J __0 _ ___ 4à 2_ 2_J 4J _ 2J __0 only at time only at the “initial” time when a time has passed since the particle’s velocity was 0 _ _ 0 2J 4 0_ 4J_2J 0_ _ 0 __ _ 2 0 _ 2J __ 0 0 0 _ 0Ã0J 0 0J 4J 2J 0 _ 0J 0J _ _ 4″ 0 _ 4J _2J0_ ____0_ 0 _ 0J” _ _ 2J” _ 2J 4J” _ 4J 0 _ 0_ 0 _ _ 2/24/2015 Assignment 2 =3484333 15/22 Part H At what time does the velocity of particle B equal that of particle A? You did not open hints for this part. ANSWER: Given Positions, Find Velocity and Acceleration Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time. The table shows the x coordinate of a moving object. The position is tabulated at 1s intervals. The x coordinate is indicated below each time. You should make the simplification that the acceleration of the object is bounded and contains no spikes. time (s) 0 1 2 3 4 5 6 7 8 9 x (m) 0 1 4 9 16 24 32 40 46 48 Part A Which graph best represents the function , describing the object’s position vs. time? 4# 0_ 4J__2J0_ _ __ 0_ 4# 0 _ 4J ____2J0__0_ 4# 0_ 4J__2J 0_0__ _ 0_ __ 0__ 4# 0 _ 4J ____2J 0_0_ __ 0_0_ _ 4# 0_ 4J__2J 0Ã0__ _ 0à __ 0__ 4# 0 _ 4J ____2J 0Ã0_ __ 0Ã0_ _ The two particles never have the same velocity. 0_ 0__ 2J __ 0__0__ 2J __ 0__0__ 2J __ 4 0 2/24/2015 Assignment 2 =3484333 16/22 You did not open hints for this part. ANSWER: Part B Which of the following graphs best represents the function , describing the object’s velocity as a function of time? You did not open hints for this part. ANSWER: 1 2 3 4 2 0 2/24/2015 Assignment 2 =3484333 17/22 Part C Which of the following graphs best represents the function , describing the acceleration of this object? You did not open hints for this part. ANSWER: A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. 1 2 3 4 _ 0 1 2 3 4 _ 0 _ _ _ _ 4 _ _ 2/24/2015 Assignment 2 =3484333 18/22 Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . You did not open hints for this part. ANSWER: Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . You did not open hints for this part. ANSWER: Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . You did not open hints for this part. 4NBO 0 _ _ 0 4NBO 0 = 4CVT 0 _ 0 4CVT = 0DBUDI 2/24/2015 Assignment 2 =3484333 19/22 ANSWER: Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Stopping on Snow Light, dry snow is called powder. Skiing on a powder day is different than skiing on a day when the snow is wet and heavy. When you slow down on dry snow the maximum (negative) acceleration caused by the snow acting on your skis is about twofifths as much as that of stopping on wet snow. Part A For a given initial velocity, how does the time it takes to stop on dry snow differ from the time it takes to stop on wet snow? You did not open hints for this part. ANSWER: Part B For a given initial velocity, how does the stopping distance on dry snow differ from the stopping distance on wet snow? 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI 4NBO 0DBUDI _ 4CVT 0DBUDI _ _ _ Ç 0DBUDI 0E 0X 0E _ ___0X 0E _ 0X 0E _ ___0X 4E 4X 2/24/2015 Assignment 2 =3484333 20/22 You did not open hints for this part. ANSWER: Exercise 2.34 A subway train starts from rest at a station and accelerates at a rate of for 14.0 . It runs at constant speed for 70.0 and slows down at a rate of until it stops at the next station. Part A Find the total distance covered. ANSWER: Problem 2.57 Dan gets on Interstate Highway I280 at Seward, Nebraska, and drives due west in a straight line and at an average velocity of magnitude 88.0 . After traveling 76 km, he reaches the Aurora exit . Realizing he has gone too far, he turns around and drives due east 34 back to the York exit at an average velocity of magnitude 75.0 . Part A For his whole trip from Seward to the York exit, what is his average speed? 4E _ ___4X 4E _ 4X 4E _ ___4X ____ N_T_ T T ____ N_T_ = LN LN_I LN LN_I 2/24/2015 Assignment 2 =3484333 21/22 ANSWER: Part B For his whole trip from Seward to the York exit, what is the magnitude of his average velocity? ANSWER: Multiple Choice Question 2.1 Part A A train starts from rest and accelerates uniformly, until it has traveled 5.9 km and acquired a velocity of 35 m/s. The train then moves at a constant velocity of 35 m/s for 400 s. The train then decelerates uniformly at 0.065 m/s2, until it is brought to a halt. The acceleration during the first 5.9 km of travel is closest to: ANSWER: Multiple Choice Question 2.8 Part A A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during collision? ANSWER: 2 = LN_I 2 = LN_I 0.13 m/s2 0.11 m/s2 0.12 m/s2 0.10 m/s2 0.093 m/s2 2/24/2015 Assignment 2 Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 18 points. zero 200 m/s2 1500 m/s2 1300 m/s2 2800 m/s2

info@checkyourstudy.com 2/24/2015 Assignment 2 =3484333 1/22 Assignment 2 Due: 6:43pm … Read More...
Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: c t = 0 b a x = 0 xman(t) b c t x(t) = x(0) + vt xman(t) = −b + ct Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: xbus(t) a t x(t) = x(0) + v(0)t + (1/2)at2 vbus(0) = 0 xbus = 1 a 2 t2 tcatch tcatch Typesetting math: 15% Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? xman(tcatch) > xbus(tcatch) xman(tcatch) = xbus(tcatch) xman(tcatch) < xbus(tcatch) c = a  tcatch xman(t) xbus(t) xman(tcatch) = xbus(tcatch) −b+ct = a catch 1 2 t2 catch 1 a −c +b = 0 2 t2 catch tcatch c tcatch cmin c a b 1 a − c + b = 0 2 t2 catch tcatch tcatch Typesetting math: 15% Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? Hint 1. What is the general quadratic equation? The general quadratic equation is , where , \texttip{B}{B}, and \texttip{C}{C} are constants. Depending on the value of the discriminant, \Delta = c^2-2ab, the equation may have Ax2 + Bx + C = 0 x = −B±B2−4AC 2A  = cc − 2ab tcatch c cmin cmin = (2ab) −−−−  c > cmin Ax2 + Bx + C = 0 A Typesetting math: 15% two real valued solutions 1. if \Delta > 0, 2. one real valued solution if \Delta = 0, or 3. two complex valued solutions if \Delta < 0. In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A No; there is no chance he is going to get aboard. Yes; he will get a second chance Typesetting math: 15% Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: C and E E and F A and F C and D B and D Typesetting math: 15% Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F Typesetting math: 15% To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector \texttip{\vec{A}}{A_vec} is decomposed into component vectors \texttip{\vec{A}_{\mit x}}{A_vec_x} and \texttip{\vec{A}_{\mit y}}{A_vec_y} parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector \texttip{\vec{A}}{A_vec}, denoted \texttip{A_{\mit x}}{A_x} and \texttip{A_{\mit y}}{A_y}. TACTICS BOX 3.1 Determining the components of a vector The absolute value |A_x| of the x component \texttip{A_{\mit x}}{A_x} is the magnitude of the component vector \texttip{\vec{A}_{\1. mit x}}{A_vec_x}. The sign of \texttip{A_{\mit x}}{A_x} is positive if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the positive x direction; it is negative if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the negative x direction. 2. 3. The y component \texttip{A_{\mit y}}{A_y} is determined similarly. Part A What is the magnitude of the component vector \texttip{\vec{A}_{\mit x}}{A_vec_x} shown in the figure? Express your answer in meters to one significant figure. ANSWER: Correct |A_x| = 5 \rm m Typesetting math: 15% Part B What is the sign of the y component \texttip{A_{\mit y}}{A_y} of vector \texttip{\vec{A}}{A_vec} shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, \texttip{B_{\mit x}}{B_x} and \texttip{B_{\mit y}}{B_y}, of vector \texttip{\vec{B}}{B_vec} shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. positive negative Typesetting math: 15% ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, \texttip{v_{\mit x}}{1. v_x}, is constant. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by \texttip{g}{g}, is equal to 9.80 \rm{m/s^2} near the surface of the earth. Hence, the y component of its velocity, \texttip{v_{\mit y}}{v_y}, changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time \texttip{t}{t} the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time t_0 = 0\;\rm{s} corresponds to the moment just after the ball is launched from position x_0 = 0\;\rm{m} and y_0 = 0\;\rm{m}. Its launch velocity, also called the initial velocity, is \texttip{\vec{v}_{\rm 0}}{v_vec_0}. Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time \texttip{t_{\rm 1}}{t_1} with velocity \texttip{\vec{v}_{\rm 1}}{v_1_vec}. Its position at this moment is denoted by (x_1, y_1) or (x_1, y_{\max}) since it is at its maximum \texttip{B_{\mit x}}{B_x}, \texttip{B_{\mit y}}{B_y} = -2,-5 \rm m, \rm m Typesetting math: 15% The other point, at time \texttip{t_{\rm 2}}{t_2} with velocity \texttip{\vec{v}_{\rm 2}}{v_2_vec}, corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is (x_2, y_2), also known as (x_{\max}, y_2) since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence y_2 = y_0 = 0\;\rm{m}. Part A How do the speeds \texttip{v_{\rm 0}}{v_0}, \texttip{v_{\rm 1}}{v_1}, and \texttip{v_{\rm 2}}{v_2} (at times \texttip{t_{\rm 0}}{t_0}, \texttip{t_{\rm 1}}{t_1}, and \texttip{t_{\rm 2}}{t_2}) compare? ANSWER: Correct Here \texttip{v_{\rm 0}}{v_0} equals \texttip{v_{\rm 2}}{v_2} by symmetry and both exceed \texttip{v_{\rm 1}}{v_1}. This is because \texttip{v_{\rm 0}}{v_0} and \texttip{v_{\rm 2}}{v_2} include vertical speed as well as the constant horizontal speed. Consider a diagram of the ball at time \texttip{t_{\rm 0}}{t_0}. Recall that \texttip{t_{\rm 0}}{t_0} refers to the instant just after the ball has been launched, so it is still at ground level (x_0 = y_0= 0\;\rm{m}). However, it is already moving with initial velocity \texttip{\vec{v}_{\rm 0}}{v_0_vec}, whose magnitude is v_0 = 30.0\;{\rm m/s} and direction is \theta = 60.0\;{\rm degrees} counterclockwise from the positive x direction. \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 1}}{v_1} = \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 1}}{v_1} > \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 Typesetting math: 15% Part B What are the values of the intial velocity vector components \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{0,x}}{a_0, x} and \texttip{a_{0,y}}{a_0, y} (both in \rm{m/s^2})? Here the subscript 0 means “at time \texttip{t_{\rm 0}}{t_0}.” Hint 1. Determining components of a vector that is aligned with an axis If a vector points along a single axis direction, such as in the positive x direction, its x component will be its full magnitude, whereas its y component will be zero since the vector is perpendicular to the y direction. If the vector points in the negative x direction, its x component will be the negative of its full magnitude. Hint 2. Calculating the components of the initial velocity Notice that the vector \texttip{\vec{v}_{\rm 0}}{v_0_vec} points up and to the right. Since “up” is the positive y axis direction and “to the right” is the positive x axis direction, \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} will both be positive. As shown in the figure, \texttip{v_{0,x}}{v_0, x}, \texttip{v_{0,y}}{v_0, y}, and \texttip{v_{\rm 0}}{v_0} are three sides of a right triangle, one angle of which is \texttip{\theta }{theta}. Thus \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} can be found using the definition of the sine and cosine functions given below. Recall that v_0 = 30.0\;\rm{m/s} and \theta = 60.0\;\rm{degrees} and note that \large{\sin(\theta) = \frac{\rm{length\;of\;opposite\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, y}}{v_0}}, \large{\cos(\theta) = \frac{\rm{length\;of\;adjacent\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, x}}{v_0}.} What are the values of \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y}? Enter your answers numerically in meters per second separated by a comma. ANSWER: ANSWER: 15.0,26.0 \rm{m/s} Typesetting math: 15% Correct Also notice that at time \texttip{t_{\rm 2}}{t_2}, just before the ball lands, its velocity components are v_{2, x} = 15\;\rm{m/s} (the same as always) and v_{2, y} = – 26.0\;\rm{m/s} (the same size but opposite sign from \texttip{v_{0,y}}{v_0, y} by symmetry). The acceleration at time \texttip{t_{\rm 2}}{t_2} will have components (0, -9.80 \rm{m/s^2}), exactly the same as at \texttip{t_{\rm 0}}{t_0}, as required by Rule 2. The peak of the trajectory occurs at time \texttip{t_{\rm 1}}{t_1}. This is the point where the ball reaches its maximum height \texttip{y_{\rm max}}{y_max}. At the peak the ball switches from moving up to moving down, even as it continues to travel horizontally at a constant rate. Part C What are the values of the velocity vector components \texttip{v_{1,x}}{v_1, x} and \texttip{v_{1,y}}{v_1, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{1,x}}{a_1, x} and \texttip{a_{1,y}}{a_1, y} (both in \rm{m/s^2})? Here the subscript 1 means that these are all at time \texttip{t_{\rm 1}}{t_1}. ANSWER: 30.0, 0, 0, 0 0, 30.0, 0, 0 15.0, 26.0, 0, 0 30.0, 0, 0, -9.80 0, 30.0, 0, -9.80 15.0, 26.0, 0, -9.80 15.0, 26.0, 0, +9.80 Typesetting math: 15% Correct At the peak of its trajectory the ball continues traveling horizontally at a constant rate. However, at this moment it stops moving up and is about to move back down. This constitutes a downward-directed change in velocity, so the ball is accelerating downward even at the peak. The flight time refers to the total amount of time the ball is in the air, from just after it is launched (\texttip{t_{\rm 0}}{t_0}) until just before it lands (\texttip{t_{\rm 2}}{t_2}). Hence the flight time can be calculated as t_2 – t_0, or just \texttip{t_{\rm 2}}{t_2} in this particular situation since t_0 = 0. Because the ball lands at the same height from which it was launched, by symmetry it spends half its flight time traveling up to the peak and the other half traveling back down. The flight time is determined by the initial vertical component of the velocity and by the acceleration. The flight time does not depend on whether the object is moving horizontally while it is in the air. Part D If a second ball were dropped from rest from height \texttip{y_{\rm max}}{y_max}, how long would it take to reach the ground? Ignore air resistance. Check all that apply. Hint 1. Kicking a ball of cliff; a related problem Consider two balls, one of which is dropped from rest off the edge of a cliff at the same moment that the other is kicked horizontally off the edge of the cliff. Which ball reaches the level ground at the base of the cliff first? Ignore air resistance. Hint 1. Comparing position, velocity, and acceleration of the two balls Both balls start at the same height and have the same initial y velocity (v_{0,y} = 0) as well as the same acceleration (\vec a = g downward). They differ only in their x velocity (one is 0, 0, 0, 0 0, 0, 0, -9.80 15.0, 0, 0, 0 15.0, 0, 0, -9.80 0, 26.0, 0, 0 0, 26.0, 0, -9.80 15.0, 26.0, 0, 0 15.0, 26.0, 0, -9.80 Typesetting math: 15% zero, the other nonzero). This difference will affect their x motion but not their y motion. ANSWER: ANSWER: Correct In projectile motion over level ground, it takes an object just as long to rise from the ground to the peak as it takes for it to fall from the peak back to the ground. The range \texttip{R}{R} of the ball refers to how far it moves horizontally, from just after it is launched until just before it lands. Range is defined as x_2 – x_0, or just \texttip{x_{\rm 2}}{x_2} in this particular situation since x_0 = 0. Range can be calculated as the product of the flight time \texttip{t_{\rm 2}}{t_2} and the x component of the velocity \texttip{v_{\mit x}}{v_x} (which is the same at all times, so v_x = v_{0,x}). The value of \texttip{v_{\mit x}}{v_x} can be found from the launch speed \texttip{v_{\rm 0}}{v_0} and the launch angle \texttip{\theta }{theta} using trigonometric functions, as was done in Part B. The flight time is related to the initial y component of the velocity, which may also be found from \texttip{v_{\rm 0}}{v_0} and \texttip{\theta }{theta} using trig functions. The following equations may be useful in solving projectile motion problems, but these equations apply only to a projectile launched over level ground from position (x_0 = y_0 = 0) at time t_0 = 0 with initial speed \texttip{v_{\rm 0}}{v_0} and launch angle \texttip{\theta }{theta} measured from the horizontal. As was the case above, \texttip{t_{\rm 2}}{t_2} refers to the flight time and \texttip{R}{R} refers to the range of the projectile. flight time: \large{t_2 = \frac{2 v_{0, y}}{g} = \frac{2 v_0 \sin(\theta)}{g}} range: \large{R = v_x t_2 = \frac{v_0^2 \sin(2\theta)}{g}} The ball that falls straight down strikes the ground first. The ball that was kicked so it moves horizontally as it falls strikes the ground first. Both balls strike the ground at the same time. \texttip{t_{\rm 0}}{t_0} t_1 – t_0 \texttip{t_{\rm 2}}{t_2} t_2 – t_1 \large{\frac{t_2 – t_0}{2}} Typesetting math: 15% In general, a high launch angle yields a long flight time but a small horizontal speed and hence little range. A low launch angle gives a larger horizontal speed, but less flight time in which to accumulate range. The launch angle that achieves the maximum range for projectile motion over level ground is 45 degrees. Part E Which of the following changes would increase the range of the ball shown in the original figure? Check all that apply. ANSWER: Correct A solid understanding of the concepts of projectile motion will take you far, including giving you additional insight into the solution of projectile motion problems numerically. Even when the object does not land at the same height from which is was launched, the rules given in the introduction will still be useful. Recall that air resistance is assumed to be negligible here, so this projectile motion analysis may not be the best choice for describing things like frisbees or feathers, whose motion is strongly influenced by air. The value of the gravitational free-fall acceleration \texttip{g}{g} is also assumed to be constant, which may not be appropriate for objects that move vertically through distances of hundreds of kilometers, like rockets or missiles. However, for problems that involve relatively dense projectiles moving close to the surface of the earth, these assumptions are reasonable. A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 15 \;{\rm m}/{\rm s}^{2}. Part A How much horizontal force \texttip{F}{F} must a sprinter of mass 64{\rm kg} exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures. Increase \texttip{v_{\rm 0}}{v_0} above 30 \rm{m/s}. Reduce \texttip{v_{\rm 0}}{v_0} below 30 \rm{m/s}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to 45 \rm{degrees}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to less than 30 \rm{degrees}. Increase \texttip{\theta }{theta} from 60 \rm{degrees} up toward 90 \rm{degrees}. Typesetting math: 15% Hint 1. Newton’s 2nd law of motion According to Newton’s 2nd law of motion, if a net external force \texttip{F_{\rm net}}{F_net} acts on a body, the body accelerates, and the net force is equal to the mass \texttip{m}{m} of the body times the acceleration \texttip{a}{a} of the body: F_{\rm net} = ma. ANSWER: Co

Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: c t = 0 b a x = 0 xman(t) b c t x(t) = x(0) + vt xman(t) = −b + ct Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: xbus(t) a t x(t) = x(0) + v(0)t + (1/2)at2 vbus(0) = 0 xbus = 1 a 2 t2 tcatch tcatch Typesetting math: 15% Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? xman(tcatch) > xbus(tcatch) xman(tcatch) = xbus(tcatch) xman(tcatch) < xbus(tcatch) c = a  tcatch xman(t) xbus(t) xman(tcatch) = xbus(tcatch) −b+ct = a catch 1 2 t2 catch 1 a −c +b = 0 2 t2 catch tcatch c tcatch cmin c a b 1 a − c + b = 0 2 t2 catch tcatch tcatch Typesetting math: 15% Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? Hint 1. What is the general quadratic equation? The general quadratic equation is , where , \texttip{B}{B}, and \texttip{C}{C} are constants. Depending on the value of the discriminant, \Delta = c^2-2ab, the equation may have Ax2 + Bx + C = 0 x = −B±B2−4AC 2A  = cc − 2ab tcatch c cmin cmin = (2ab) −−−−  c > cmin Ax2 + Bx + C = 0 A Typesetting math: 15% two real valued solutions 1. if \Delta > 0, 2. one real valued solution if \Delta = 0, or 3. two complex valued solutions if \Delta < 0. In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A No; there is no chance he is going to get aboard. Yes; he will get a second chance Typesetting math: 15% Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: C and E E and F A and F C and D B and D Typesetting math: 15% Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F Typesetting math: 15% To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector \texttip{\vec{A}}{A_vec} is decomposed into component vectors \texttip{\vec{A}_{\mit x}}{A_vec_x} and \texttip{\vec{A}_{\mit y}}{A_vec_y} parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector \texttip{\vec{A}}{A_vec}, denoted \texttip{A_{\mit x}}{A_x} and \texttip{A_{\mit y}}{A_y}. TACTICS BOX 3.1 Determining the components of a vector The absolute value |A_x| of the x component \texttip{A_{\mit x}}{A_x} is the magnitude of the component vector \texttip{\vec{A}_{\1. mit x}}{A_vec_x}. The sign of \texttip{A_{\mit x}}{A_x} is positive if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the positive x direction; it is negative if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the negative x direction. 2. 3. The y component \texttip{A_{\mit y}}{A_y} is determined similarly. Part A What is the magnitude of the component vector \texttip{\vec{A}_{\mit x}}{A_vec_x} shown in the figure? Express your answer in meters to one significant figure. ANSWER: Correct |A_x| = 5 \rm m Typesetting math: 15% Part B What is the sign of the y component \texttip{A_{\mit y}}{A_y} of vector \texttip{\vec{A}}{A_vec} shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, \texttip{B_{\mit x}}{B_x} and \texttip{B_{\mit y}}{B_y}, of vector \texttip{\vec{B}}{B_vec} shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. positive negative Typesetting math: 15% ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, \texttip{v_{\mit x}}{1. v_x}, is constant. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by \texttip{g}{g}, is equal to 9.80 \rm{m/s^2} near the surface of the earth. Hence, the y component of its velocity, \texttip{v_{\mit y}}{v_y}, changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time \texttip{t}{t} the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time t_0 = 0\;\rm{s} corresponds to the moment just after the ball is launched from position x_0 = 0\;\rm{m} and y_0 = 0\;\rm{m}. Its launch velocity, also called the initial velocity, is \texttip{\vec{v}_{\rm 0}}{v_vec_0}. Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time \texttip{t_{\rm 1}}{t_1} with velocity \texttip{\vec{v}_{\rm 1}}{v_1_vec}. Its position at this moment is denoted by (x_1, y_1) or (x_1, y_{\max}) since it is at its maximum \texttip{B_{\mit x}}{B_x}, \texttip{B_{\mit y}}{B_y} = -2,-5 \rm m, \rm m Typesetting math: 15% The other point, at time \texttip{t_{\rm 2}}{t_2} with velocity \texttip{\vec{v}_{\rm 2}}{v_2_vec}, corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is (x_2, y_2), also known as (x_{\max}, y_2) since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence y_2 = y_0 = 0\;\rm{m}. Part A How do the speeds \texttip{v_{\rm 0}}{v_0}, \texttip{v_{\rm 1}}{v_1}, and \texttip{v_{\rm 2}}{v_2} (at times \texttip{t_{\rm 0}}{t_0}, \texttip{t_{\rm 1}}{t_1}, and \texttip{t_{\rm 2}}{t_2}) compare? ANSWER: Correct Here \texttip{v_{\rm 0}}{v_0} equals \texttip{v_{\rm 2}}{v_2} by symmetry and both exceed \texttip{v_{\rm 1}}{v_1}. This is because \texttip{v_{\rm 0}}{v_0} and \texttip{v_{\rm 2}}{v_2} include vertical speed as well as the constant horizontal speed. Consider a diagram of the ball at time \texttip{t_{\rm 0}}{t_0}. Recall that \texttip{t_{\rm 0}}{t_0} refers to the instant just after the ball has been launched, so it is still at ground level (x_0 = y_0= 0\;\rm{m}). However, it is already moving with initial velocity \texttip{\vec{v}_{\rm 0}}{v_0_vec}, whose magnitude is v_0 = 30.0\;{\rm m/s} and direction is \theta = 60.0\;{\rm degrees} counterclockwise from the positive x direction. \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 1}}{v_1} = \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 1}}{v_1} > \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 Typesetting math: 15% Part B What are the values of the intial velocity vector components \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{0,x}}{a_0, x} and \texttip{a_{0,y}}{a_0, y} (both in \rm{m/s^2})? Here the subscript 0 means “at time \texttip{t_{\rm 0}}{t_0}.” Hint 1. Determining components of a vector that is aligned with an axis If a vector points along a single axis direction, such as in the positive x direction, its x component will be its full magnitude, whereas its y component will be zero since the vector is perpendicular to the y direction. If the vector points in the negative x direction, its x component will be the negative of its full magnitude. Hint 2. Calculating the components of the initial velocity Notice that the vector \texttip{\vec{v}_{\rm 0}}{v_0_vec} points up and to the right. Since “up” is the positive y axis direction and “to the right” is the positive x axis direction, \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} will both be positive. As shown in the figure, \texttip{v_{0,x}}{v_0, x}, \texttip{v_{0,y}}{v_0, y}, and \texttip{v_{\rm 0}}{v_0} are three sides of a right triangle, one angle of which is \texttip{\theta }{theta}. Thus \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} can be found using the definition of the sine and cosine functions given below. Recall that v_0 = 30.0\;\rm{m/s} and \theta = 60.0\;\rm{degrees} and note that \large{\sin(\theta) = \frac{\rm{length\;of\;opposite\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, y}}{v_0}}, \large{\cos(\theta) = \frac{\rm{length\;of\;adjacent\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, x}}{v_0}.} What are the values of \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y}? Enter your answers numerically in meters per second separated by a comma. ANSWER: ANSWER: 15.0,26.0 \rm{m/s} Typesetting math: 15% Correct Also notice that at time \texttip{t_{\rm 2}}{t_2}, just before the ball lands, its velocity components are v_{2, x} = 15\;\rm{m/s} (the same as always) and v_{2, y} = – 26.0\;\rm{m/s} (the same size but opposite sign from \texttip{v_{0,y}}{v_0, y} by symmetry). The acceleration at time \texttip{t_{\rm 2}}{t_2} will have components (0, -9.80 \rm{m/s^2}), exactly the same as at \texttip{t_{\rm 0}}{t_0}, as required by Rule 2. The peak of the trajectory occurs at time \texttip{t_{\rm 1}}{t_1}. This is the point where the ball reaches its maximum height \texttip{y_{\rm max}}{y_max}. At the peak the ball switches from moving up to moving down, even as it continues to travel horizontally at a constant rate. Part C What are the values of the velocity vector components \texttip{v_{1,x}}{v_1, x} and \texttip{v_{1,y}}{v_1, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{1,x}}{a_1, x} and \texttip{a_{1,y}}{a_1, y} (both in \rm{m/s^2})? Here the subscript 1 means that these are all at time \texttip{t_{\rm 1}}{t_1}. ANSWER: 30.0, 0, 0, 0 0, 30.0, 0, 0 15.0, 26.0, 0, 0 30.0, 0, 0, -9.80 0, 30.0, 0, -9.80 15.0, 26.0, 0, -9.80 15.0, 26.0, 0, +9.80 Typesetting math: 15% Correct At the peak of its trajectory the ball continues traveling horizontally at a constant rate. However, at this moment it stops moving up and is about to move back down. This constitutes a downward-directed change in velocity, so the ball is accelerating downward even at the peak. The flight time refers to the total amount of time the ball is in the air, from just after it is launched (\texttip{t_{\rm 0}}{t_0}) until just before it lands (\texttip{t_{\rm 2}}{t_2}). Hence the flight time can be calculated as t_2 – t_0, or just \texttip{t_{\rm 2}}{t_2} in this particular situation since t_0 = 0. Because the ball lands at the same height from which it was launched, by symmetry it spends half its flight time traveling up to the peak and the other half traveling back down. The flight time is determined by the initial vertical component of the velocity and by the acceleration. The flight time does not depend on whether the object is moving horizontally while it is in the air. Part D If a second ball were dropped from rest from height \texttip{y_{\rm max}}{y_max}, how long would it take to reach the ground? Ignore air resistance. Check all that apply. Hint 1. Kicking a ball of cliff; a related problem Consider two balls, one of which is dropped from rest off the edge of a cliff at the same moment that the other is kicked horizontally off the edge of the cliff. Which ball reaches the level ground at the base of the cliff first? Ignore air resistance. Hint 1. Comparing position, velocity, and acceleration of the two balls Both balls start at the same height and have the same initial y velocity (v_{0,y} = 0) as well as the same acceleration (\vec a = g downward). They differ only in their x velocity (one is 0, 0, 0, 0 0, 0, 0, -9.80 15.0, 0, 0, 0 15.0, 0, 0, -9.80 0, 26.0, 0, 0 0, 26.0, 0, -9.80 15.0, 26.0, 0, 0 15.0, 26.0, 0, -9.80 Typesetting math: 15% zero, the other nonzero). This difference will affect their x motion but not their y motion. ANSWER: ANSWER: Correct In projectile motion over level ground, it takes an object just as long to rise from the ground to the peak as it takes for it to fall from the peak back to the ground. The range \texttip{R}{R} of the ball refers to how far it moves horizontally, from just after it is launched until just before it lands. Range is defined as x_2 – x_0, or just \texttip{x_{\rm 2}}{x_2} in this particular situation since x_0 = 0. Range can be calculated as the product of the flight time \texttip{t_{\rm 2}}{t_2} and the x component of the velocity \texttip{v_{\mit x}}{v_x} (which is the same at all times, so v_x = v_{0,x}). The value of \texttip{v_{\mit x}}{v_x} can be found from the launch speed \texttip{v_{\rm 0}}{v_0} and the launch angle \texttip{\theta }{theta} using trigonometric functions, as was done in Part B. The flight time is related to the initial y component of the velocity, which may also be found from \texttip{v_{\rm 0}}{v_0} and \texttip{\theta }{theta} using trig functions. The following equations may be useful in solving projectile motion problems, but these equations apply only to a projectile launched over level ground from position (x_0 = y_0 = 0) at time t_0 = 0 with initial speed \texttip{v_{\rm 0}}{v_0} and launch angle \texttip{\theta }{theta} measured from the horizontal. As was the case above, \texttip{t_{\rm 2}}{t_2} refers to the flight time and \texttip{R}{R} refers to the range of the projectile. flight time: \large{t_2 = \frac{2 v_{0, y}}{g} = \frac{2 v_0 \sin(\theta)}{g}} range: \large{R = v_x t_2 = \frac{v_0^2 \sin(2\theta)}{g}} The ball that falls straight down strikes the ground first. The ball that was kicked so it moves horizontally as it falls strikes the ground first. Both balls strike the ground at the same time. \texttip{t_{\rm 0}}{t_0} t_1 – t_0 \texttip{t_{\rm 2}}{t_2} t_2 – t_1 \large{\frac{t_2 – t_0}{2}} Typesetting math: 15% In general, a high launch angle yields a long flight time but a small horizontal speed and hence little range. A low launch angle gives a larger horizontal speed, but less flight time in which to accumulate range. The launch angle that achieves the maximum range for projectile motion over level ground is 45 degrees. Part E Which of the following changes would increase the range of the ball shown in the original figure? Check all that apply. ANSWER: Correct A solid understanding of the concepts of projectile motion will take you far, including giving you additional insight into the solution of projectile motion problems numerically. Even when the object does not land at the same height from which is was launched, the rules given in the introduction will still be useful. Recall that air resistance is assumed to be negligible here, so this projectile motion analysis may not be the best choice for describing things like frisbees or feathers, whose motion is strongly influenced by air. The value of the gravitational free-fall acceleration \texttip{g}{g} is also assumed to be constant, which may not be appropriate for objects that move vertically through distances of hundreds of kilometers, like rockets or missiles. However, for problems that involve relatively dense projectiles moving close to the surface of the earth, these assumptions are reasonable. A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 15 \;{\rm m}/{\rm s}^{2}. Part A How much horizontal force \texttip{F}{F} must a sprinter of mass 64{\rm kg} exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures. Increase \texttip{v_{\rm 0}}{v_0} above 30 \rm{m/s}. Reduce \texttip{v_{\rm 0}}{v_0} below 30 \rm{m/s}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to 45 \rm{degrees}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to less than 30 \rm{degrees}. Increase \texttip{\theta }{theta} from 60 \rm{degrees} up toward 90 \rm{degrees}. Typesetting math: 15% Hint 1. Newton’s 2nd law of motion According to Newton’s 2nd law of motion, if a net external force \texttip{F_{\rm net}}{F_net} acts on a body, the body accelerates, and the net force is equal to the mass \texttip{m}{m} of the body times the acceleration \texttip{a}{a} of the body: F_{\rm net} = ma. ANSWER: Co

please email info@checkyourstudy.com
All answers should be in radians not degrees. 1) (15 pts total) Conditional Probability Two integrated circuits made from the same wafer are tested. Each IC either passes the test or fails the test. The event that the first IC fails the test is called A. The event that the second IC fails the test is called B. The probability of A, P(A)=0.02. The probability of B, P(B)=0.02. The probability that both ICs fail is ?(?∩?)?? 0.01. What is the conditional probability P(B|A) the the 2nd IC fails the test given that the first IC failed the test? 2) (20 points total) Sampling with replacement The NAU student ID number is a 7-digit number. Assume all numbers are randomly generated, and all numbers are equally likely to be generated. a) (5 ???) How many possible student ID numbers are there? b) (5 ???) What is the probability of getting the ID number that is all 1s, 1111111? c) (5 ???) How many student ID numbers have a 1 as the first digit? d) (5 ???) What is the probability of getting a student ID number with a 1 as the first digit? 3) (15 pts total) Sampling without replacement A box in the EE188 lab contains 200 resistors that are labeled 100kΩ resistors. Five of these resistors are in fact 10 kΩ resistors (only 5!) Your circuit design uses 3 100 kΩ resistors. a) (5 pts) What is the probability that all 3 of the resistors you choose are 100kΩ resistors? b) (5 pts) What is the probability that one or more or the 3 resistors that you chose aren’t 100 kΩ resistors? Hint: use the answer from part a) c) (5 pts) What is the probability that all 3 resistors that you chose are not 100 kΩ resistors. 4) (20 pts total) Combinations: Arrangements where order doesn’t matter a) (3 pts) How many ways are there to draw 3 resistors from a box of 200 resistors? b) (3 pts) How many ways are there to draw 3 resistors from a group of 195 100 kΩ resistors? c) (4 pts) Calculate the probability of drawing 3 100 kΩ resistors from a box of 200 resistors, where 195 are 100 kΩ resistors and 5 are 10 kΩ resistors. Use your results from a) and b) to find this probability. d) (2 pts) Is your answer in c) the same as 3a)? e) (3 pts) How many ways are there to draw 3 resistors from a group of 5 10 kΩ resistors? f) (3 pts) Calculate the probability of drawing 3 10 kΩ resistors from a box of 200 resistors, where 195 are 100 kΩ resistors and 5 are 10 kΩ resistors. Use your results from a) and e) to find this probability. g) (2 pts) Is your answer in f) the same as your answer from 3c)? 5) (20 pts) For the following data set: 70.6, 70.9, 69.1, 71.3, 70.5, 69.7, 71.5, 69.8, 71.1, 68.9, 70.3, 69.2, 71.2, 70.4, 72.8 a) (5 pts) Draw a histogram with bin size 0.5, starting at the bin 68.45-68.95 b) (5 pts) What is the mean of the data? c) (5 pts) What is the median of the data? d) (5 pts) What is the standard deviation of the data?

All answers should be in radians not degrees. 1) (15 pts total) Conditional Probability Two integrated circuits made from the same wafer are tested. Each IC either passes the test or fails the test. The event that the first IC fails the test is called A. The event that the second IC fails the test is called B. The probability of A, P(A)=0.02. The probability of B, P(B)=0.02. The probability that both ICs fail is ?(?∩?)?? 0.01. What is the conditional probability P(B|A) the the 2nd IC fails the test given that the first IC failed the test? 2) (20 points total) Sampling with replacement The NAU student ID number is a 7-digit number. Assume all numbers are randomly generated, and all numbers are equally likely to be generated. a) (5 ???) How many possible student ID numbers are there? b) (5 ???) What is the probability of getting the ID number that is all 1s, 1111111? c) (5 ???) How many student ID numbers have a 1 as the first digit? d) (5 ???) What is the probability of getting a student ID number with a 1 as the first digit? 3) (15 pts total) Sampling without replacement A box in the EE188 lab contains 200 resistors that are labeled 100kΩ resistors. Five of these resistors are in fact 10 kΩ resistors (only 5!) Your circuit design uses 3 100 kΩ resistors. a) (5 pts) What is the probability that all 3 of the resistors you choose are 100kΩ resistors? b) (5 pts) What is the probability that one or more or the 3 resistors that you chose aren’t 100 kΩ resistors? Hint: use the answer from part a) c) (5 pts) What is the probability that all 3 resistors that you chose are not 100 kΩ resistors. 4) (20 pts total) Combinations: Arrangements where order doesn’t matter a) (3 pts) How many ways are there to draw 3 resistors from a box of 200 resistors? b) (3 pts) How many ways are there to draw 3 resistors from a group of 195 100 kΩ resistors? c) (4 pts) Calculate the probability of drawing 3 100 kΩ resistors from a box of 200 resistors, where 195 are 100 kΩ resistors and 5 are 10 kΩ resistors. Use your results from a) and b) to find this probability. d) (2 pts) Is your answer in c) the same as 3a)? e) (3 pts) How many ways are there to draw 3 resistors from a group of 5 10 kΩ resistors? f) (3 pts) Calculate the probability of drawing 3 10 kΩ resistors from a box of 200 resistors, where 195 are 100 kΩ resistors and 5 are 10 kΩ resistors. Use your results from a) and e) to find this probability. g) (2 pts) Is your answer in f) the same as your answer from 3c)? 5) (20 pts) For the following data set: 70.6, 70.9, 69.1, 71.3, 70.5, 69.7, 71.5, 69.8, 71.1, 68.9, 70.3, 69.2, 71.2, 70.4, 72.8 a) (5 pts) Draw a histogram with bin size 0.5, starting at the bin 68.45-68.95 b) (5 pts) What is the mean of the data? c) (5 pts) What is the median of the data? d) (5 pts) What is the standard deviation of the data?

No expert has answered this question yet. You can browse … 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

please email info@checkyourstudy.com
Programming Assignment 7: Poker (5-Card Draw) II. Prerequisites: Before starting this programming assignment, participants should be able to: Apply and implement pointers in C Pass output parameters to functions Analyze a basic set of requirements and apply top-down design principles for a problem Apply repetition structures within an algorithm Construct while (), for (), or do-while () loops in C Compose C programs consisting of sequential, conditional, and iterative statements Eliminate redundancy within a program by applying loops and functions Create structure charts for a given problem Open and close files Read, write to, and update files Manipulate file handles Apply standard library functions: fopen (), fclose (), fscanf (), and fprintf () Apply and implement pointers 2-dimenional arrays Define and apply structs in C Compose decision statements (“if” conditional statements) Create and utilize compound conditions Summarize topics from Hanly & Koffman Chapter 8 including: What is an array? Distinguishing between single dimensional and 2-dimentional arrays What is an index? III. Overview & Requirements: Write a program that allows a user to play 5-Card-Draw Poker against the computer. Start with the following example code supplied by Deitel & Deitel (example code). This will help you get started with the game of Poker. Please read this site to learn the rules of Poker http://en.wikipedia.org/wiki/5_card_draw. Complete the following step and you will have a working Poker game!!! Adapted from Deitel & Deitel’s C How to Program (6th Edition): (1) In order to complete the game of 5-card-draw poker, you should complete the following functions: (a) (5 pts) Modify the card dealing function provided in the example code so that a five-card poker hand is dealt. (b) (5 pts) Write a function to determine if the hand contains a pair. (c) (5 pts) Write a function to determine if the hand contains two pairs. (d) (5 pts) Write a function to determine if the hand contains three of a kind (e.g. three jacks). (e) (5 pts) Write a function to determine if the hand contains four of a kind (e.g. four aces). (f) (5 pts) Write a function to determine if the hand contains a flush (i.e. all five cards of the same suit). (g) (5 pts) Write a function to determine if the hand contains a straight (i.e. five cards of consecutive face values). (2) (20 pts) Use the functions developed in (1) to deal two five-card poker hands, evaluate each hand, and determine which is the better hand. (3) (25 pts) Simulate the dealer. The dealer’s five-card hand is dealt “face down” so the player cannot see it. The program should then evaluate the dealer’s hand, and based on the quality of the hand, the dealer should draw one, two, or three more cards to replace the corresponding number of unneeded cards in the original hand. The program should then re-evaluate the dealer’s hand. (4) (10 pts) Make the program handle the dealer’s five-card hand automatically. The player should be allowed to decide which cards of the player’s hand to replace. The program should then evaluate both hands and determine who wins. Now use the program to play 10 games against the computer. You should be able to test and modify or refine your Poker game based on these results!

Programming Assignment 7: Poker (5-Card Draw) II. Prerequisites: Before starting this programming assignment, participants should be able to: Apply and implement pointers in C Pass output parameters to functions Analyze a basic set of requirements and apply top-down design principles for a problem Apply repetition structures within an algorithm Construct while (), for (), or do-while () loops in C Compose C programs consisting of sequential, conditional, and iterative statements Eliminate redundancy within a program by applying loops and functions Create structure charts for a given problem Open and close files Read, write to, and update files Manipulate file handles Apply standard library functions: fopen (), fclose (), fscanf (), and fprintf () Apply and implement pointers 2-dimenional arrays Define and apply structs in C Compose decision statements (“if” conditional statements) Create and utilize compound conditions Summarize topics from Hanly & Koffman Chapter 8 including: What is an array? Distinguishing between single dimensional and 2-dimentional arrays What is an index? III. Overview & Requirements: Write a program that allows a user to play 5-Card-Draw Poker against the computer. Start with the following example code supplied by Deitel & Deitel (example code). This will help you get started with the game of Poker. Please read this site to learn the rules of Poker http://en.wikipedia.org/wiki/5_card_draw. Complete the following step and you will have a working Poker game!!! Adapted from Deitel & Deitel’s C How to Program (6th Edition): (1) In order to complete the game of 5-card-draw poker, you should complete the following functions: (a) (5 pts) Modify the card dealing function provided in the example code so that a five-card poker hand is dealt. (b) (5 pts) Write a function to determine if the hand contains a pair. (c) (5 pts) Write a function to determine if the hand contains two pairs. (d) (5 pts) Write a function to determine if the hand contains three of a kind (e.g. three jacks). (e) (5 pts) Write a function to determine if the hand contains four of a kind (e.g. four aces). (f) (5 pts) Write a function to determine if the hand contains a flush (i.e. all five cards of the same suit). (g) (5 pts) Write a function to determine if the hand contains a straight (i.e. five cards of consecutive face values). (2) (20 pts) Use the functions developed in (1) to deal two five-card poker hands, evaluate each hand, and determine which is the better hand. (3) (25 pts) Simulate the dealer. The dealer’s five-card hand is dealt “face down” so the player cannot see it. The program should then evaluate the dealer’s hand, and based on the quality of the hand, the dealer should draw one, two, or three more cards to replace the corresponding number of unneeded cards in the original hand. The program should then re-evaluate the dealer’s hand. (4) (10 pts) Make the program handle the dealer’s five-card hand automatically. The player should be allowed to decide which cards of the player’s hand to replace. The program should then evaluate both hands and determine who wins. Now use the program to play 10 games against the computer. You should be able to test and modify or refine your Poker game based on these results!

checkyourstudy.com Whatsapp +919911743277
Determine the maximum theoritical speed that may be achieved over a distance of 110 m by a car starting from rest assuming there is no slipping. The cofficient of static friction between the tires and pavement is 0.75 .assume (a) front-wheel drive, (b) near-wheel drive.

Determine the maximum theoritical speed that may be achieved over a distance of 110 m by a car starting from rest assuming there is no slipping. The cofficient of static friction between the tires and pavement is 0.75 .assume (a) front-wheel drive, (b) near-wheel drive.