13. Last year, Delip Industries had (1) negative cash flow from operations, (2) a negative free cash flow, and (3) an increase in cash as reported on its balance sheet. Which of the following factors could explain this situation? a. The company had a sharp increase in its inventories. b. The company had a sharp increase in its accrued liabilities. c. The company sold a new issue of common stock. d. The company made a large capital investment early in the year. e. The company had a sharp increase in depreciation expenses.13. Last year, Delip Industries had (1) negative cash flow from operations, (2) a negative free cash flow, and (3) an increase in cash as reported on its balance sheet. Which of the following factors could explain this situation? a. The company had a sharp increase in its inventories. b. The company had a sharp increase in its accrued liabilities. c. The company sold a new issue of common stock. d. The company made a large capital investment early in the year. e. The company had a sharp increase in depreciation expenses.

13. Last year, Delip Industries had (1) negative cash flow from operations, (2) a negative free cash flow, and (3) an increase in cash as reported on its balance sheet. Which of the following factors could explain this situation? a. The company had a sharp increase in its inventories. b. The company had a sharp increase in its accrued liabilities. c. The company sold a new issue of common stock. d. The company made a large capital investment early in the year. e. The company had a sharp increase in depreciation expenses.13. Last year, Delip Industries had (1) negative cash flow from operations, (2) a negative free cash flow, and (3) an increase in cash as reported on its balance sheet. Which of the following factors could explain this situation? a. The company had a sharp increase in its inventories. b. The company had a sharp increase in its accrued liabilities. c. The company sold a new issue of common stock. d. The company made a large capital investment early in the year. e. The company had a sharp increase in depreciation expenses.

Answer: c 13.    Last year, Delip Industries had (1) negative … Read More...
Quiz Page 1 of 2 Note: It is recommended that you save your response as you complete each question. ________________________________________ Question 1 (1 point) Which of the following can cause cervicitis? Question 1 options: Candida Sexually transmitted infections Irritation from a contraceptive All of these choices are correct Question 2 (1 point) There is every indication that cervical cancer may take _____ or more years to develop. Question 2 options: 5 15 2 10 Question 3 (1 point) Cervical cancer is found almost exclusively in women who have been Question 3 options: sexually active underweight celibate overweight Question 4 (1 point) The best predictor for survival of ovarian cancer is Question 4 options: the sexual history of the patient how far the tumor has spread the amount of diagnostic measures taken the attitude (positive or negative) of the patient Question 5 (1 point) The current recommendation for most women, after becoming sexually active or starting at age 21, is to have a Pap smear done Question 5 options: once every 3 years once every year once every 5 years once every 6 months Page 1 of 2 ________________________________________ Quiz Page 2 of 2 Note: It is recommended that you save your response as you complete each question. Question 6 (1 point) Which of the following is not a fibroid classification? Question 6 options: Submucous Subserous Extramural Intramural Question 7 (1 point) Statistics indicate that _____ of breast cancers are diagnosed when women are between 45 and 64 years of age. Question 7 options: 47% 14% 22% 35% Question 8 (1 point) Ovarian cancers are classified according to their: Question 8 options: Cellular origin Symptoms Genetic predispositions All of these choices are correct Question 9 (1 point) The primary initial symptom of endometrial cancer is Question 9 options: odiferous vaginal discharge abnormal and painless vaginal bleeding painful, often incapacitating, cramps involuntary uterine contractions Question 10 (1 point) Ovarian cancers are considered the worst of gynecological malignancies because Question 10 options: they sometimes develop slowly they are often symptomless until it is too late too little is known about this disease both A and B are correct choices Page 2 of 2 Quiz 8 Quiz Page 2 of 2 Note: It is recommended that you save your response as you complete each question. Question 6 (1 point) The best predictor for survival of ovarian cancer is Question 6 options: the sexual history of the patient how far the tumor has spread the attitude (positive or negative) of the patient the amount of diagnostic measures taken Question 7 (1 point) Ovarian cancers are classified according to their: Question 7 options: Genetic predispositions Symptoms Cellular origin All of these choices are correct Question 8 (1 point) The primary initial symptom of endometrial cancer is Question 8 options: involuntary uterine contractions painful, often incapacitating, cramps abnormal and painless vaginal bleeding odiferous vaginal discharge Question 9 (1 point) Cervical cancer is found almost exclusively in women who have been Question 9 options: sexually active underweight celibate overweight Question 10 (1 point) Several screening techniques for early detection of ovarian cancer have been developed. As of yet _____ have proven effective. Question 10 options: 50% All None 25% Page 2 of 2 ________________________________________ Quiz Page 1 of 2 Note: It is recommended that you save your response as you complete each question. ________________________________________ Question 1 (1 point) The unsubstantiated idea that the uterus was damaged by sports and emotions remained common into the: Question 1 options: 1890s 1950s 1920s 1970s Question 2 (1 point) Which of the following can cause cervicitis? Question 2 options: Candida Sexually transmitted infections Irritation from a contraceptive All of these choices are correct Question 3 (1 point) There is every indication that cervical cancer may take _____ or more years to develop. Question 3 options: 10 5 2 15 Question 4 (1 point) Which of the following is not a fibroid classification? Question 4 options: Intramural Subserous Extramural Submucous Question 5 (1 point) Ovarian cancers are considered the worst of gynecological malignancies because Question 5 options: they sometimes develop slowly they are often symptomless until it is too late too little is known about this disease both A and B are correct choices Page 1 of 2 ________________________________________

Quiz Page 1 of 2 Note: It is recommended that you save your response as you complete each question. ________________________________________ Question 1 (1 point) Which of the following can cause cervicitis? Question 1 options: Candida Sexually transmitted infections Irritation from a contraceptive All of these choices are correct Question 2 (1 point) There is every indication that cervical cancer may take _____ or more years to develop. Question 2 options: 5 15 2 10 Question 3 (1 point) Cervical cancer is found almost exclusively in women who have been Question 3 options: sexually active underweight celibate overweight Question 4 (1 point) The best predictor for survival of ovarian cancer is Question 4 options: the sexual history of the patient how far the tumor has spread the amount of diagnostic measures taken the attitude (positive or negative) of the patient Question 5 (1 point) The current recommendation for most women, after becoming sexually active or starting at age 21, is to have a Pap smear done Question 5 options: once every 3 years once every year once every 5 years once every 6 months Page 1 of 2 ________________________________________ Quiz Page 2 of 2 Note: It is recommended that you save your response as you complete each question. Question 6 (1 point) Which of the following is not a fibroid classification? Question 6 options: Submucous Subserous Extramural Intramural Question 7 (1 point) Statistics indicate that _____ of breast cancers are diagnosed when women are between 45 and 64 years of age. Question 7 options: 47% 14% 22% 35% Question 8 (1 point) Ovarian cancers are classified according to their: Question 8 options: Cellular origin Symptoms Genetic predispositions All of these choices are correct Question 9 (1 point) The primary initial symptom of endometrial cancer is Question 9 options: odiferous vaginal discharge abnormal and painless vaginal bleeding painful, often incapacitating, cramps involuntary uterine contractions Question 10 (1 point) Ovarian cancers are considered the worst of gynecological malignancies because Question 10 options: they sometimes develop slowly they are often symptomless until it is too late too little is known about this disease both A and B are correct choices Page 2 of 2 Quiz 8 Quiz Page 2 of 2 Note: It is recommended that you save your response as you complete each question. Question 6 (1 point) The best predictor for survival of ovarian cancer is Question 6 options: the sexual history of the patient how far the tumor has spread the attitude (positive or negative) of the patient the amount of diagnostic measures taken Question 7 (1 point) Ovarian cancers are classified according to their: Question 7 options: Genetic predispositions Symptoms Cellular origin All of these choices are correct Question 8 (1 point) The primary initial symptom of endometrial cancer is Question 8 options: involuntary uterine contractions painful, often incapacitating, cramps abnormal and painless vaginal bleeding odiferous vaginal discharge Question 9 (1 point) Cervical cancer is found almost exclusively in women who have been Question 9 options: sexually active underweight celibate overweight Question 10 (1 point) Several screening techniques for early detection of ovarian cancer have been developed. As of yet _____ have proven effective. Question 10 options: 50% All None 25% Page 2 of 2 ________________________________________ Quiz Page 1 of 2 Note: It is recommended that you save your response as you complete each question. ________________________________________ Question 1 (1 point) The unsubstantiated idea that the uterus was damaged by sports and emotions remained common into the: Question 1 options: 1890s 1950s 1920s 1970s Question 2 (1 point) Which of the following can cause cervicitis? Question 2 options: Candida Sexually transmitted infections Irritation from a contraceptive All of these choices are correct Question 3 (1 point) There is every indication that cervical cancer may take _____ or more years to develop. Question 3 options: 10 5 2 15 Question 4 (1 point) Which of the following is not a fibroid classification? Question 4 options: Intramural Subserous Extramural Submucous Question 5 (1 point) Ovarian cancers are considered the worst of gynecological malignancies because Question 5 options: they sometimes develop slowly they are often symptomless until it is too late too little is known about this disease both A and B are correct choices Page 1 of 2 ________________________________________

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Two charges are arranged . If Q1 is negative, and the net electric fields at point A points left, then. a) Q2 is positive ; and |Q2|>|Q1||, b) Q2 is positive ; and |Q2||Q1|, e) Q2 is negative ; and |Q2|<|Q1|

Two charges are arranged . If Q1 is negative, and the net electric fields at point A points left, then. a) Q2 is positive ; and |Q2|>|Q1||, b) Q2 is positive ; and |Q2||Q1|, e) Q2 is negative ; and |Q2|<|Q1|

Chapter 4 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Advice for the Quarterback A quarterback is set up to throw the football to a receiver who is running with a constant velocity directly away from the quarterback and is now a distance away from the quarterback. The quarterback figures that the ball must be thrown at an angle to the horizontal and he estimates that the receiver must catch the ball a time interval after it is thrown to avoid having opposition players prevent the receiver from making the catch. In the following you may assume that the ball is thrown and caught at the same height above the level playing field. Assume that the y coordinate of the ball at the instant it is thrown or caught is and that the horizontal position of the quaterback is . Use for the magnitude of the acceleration due to gravity, and use the pictured inertial coordinate system when solving the problem. Part A Find , the vertical component of the velocity of the ball when the quarterback releases it. Express in terms of and . Hint 1. Equation of motion in y direction What is the expression for , the height of the ball as a function of time? Answer in terms of , , and . v r D  tc y = 0 x = 0 g v0y v0y tc g y(t) t g v0y ANSWER: Incorrect; Try Again Hint 2. Height at which the ball is caught, Remember that after time the ball was caught at the same height as it had been released. That is, . ANSWER: Answer Requested Part B Find , the initial horizontal component of velocity of the ball. Express your answer for in terms of , , and . Hint 1. Receiver’s position Find , the receiver’s position before he catches the ball. Answer in terms of , , and . ANSWER: Football’s position y(t) = v0yt− g 1 2 t2 y(tc) tc y(tc) = y0 = 0 v0y = gtc 2 v0x v0x D tc vr xr D vr tc xr = D + vrtc Typesetting math: 100% Find , the horizontal distance that the ball travels before reaching the receiver. Answer in terms of and . ANSWER: ANSWER: Answer Requested Part C Find the speed with which the quarterback must throw the ball. Answer in terms of , , , and . Hint 1. How to approach the problem Remember that velocity is a vector; from solving Parts A and B you have the two components, from which you can find the magnitude of this vector. ANSWER: Answer Requested Part D xc v0x tc xc = v0xtc v0x = + D tc vr v0 D tc vr g v0 = ( + ) + D tc vr 2 ( ) gtc 2 2 −−−−−−−−−−−−−−−−−−−  Typesetting math: 100% Assuming that the quarterback throws the ball with speed , find the angle above the horizontal at which he should throw it. Your solution should contain an inverse trig function (entered as asin, acos, or atan). Give your answer in terms of already known quantities, , , and . Hint 1. Find angle from and Think of velocity as a vector with Cartesian coordinates and . Find the angle that this vector would make with the x axis using the results of Parts A and B. ANSWER: Answer Requested Direction of Velocity at Various Times in Flight for Projectile Motion Conceptual Question For each of the motions described below, determine the algebraic sign (positive, negative, or zero) of the x component and y component of velocity of the object at the time specified. For all of the motions, the positive x axis points to the right and the positive y axis points upward. Alex, a mountaineer, must leap across a wide crevasse. The other side of the crevasse is below the point from which he leaps, as shown in the figure. Alex leaps horizontally and successfully makes the jump. v0  v0x v0y v0  v0x v0y v0xx^ v0yy^   = atan( ) v0y v0x Typesetting math: 100% Part A Determine the algebraic sign of Alex’s x velocity and y velocity at the instant he leaves the ground at the beginning of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Algebraic sign of velocity The algebraic sign of the velocity is determined solely by comparing the direction in which the object is moving with the direction that is defined to be positive. In this example, to the right is defined to be the positive x direction and upward the positive y direction. Therefore, any object moving to the right, whether speeding up, slowing down, or even simultaneously moving upward or downward, has a positive x velocity. Similarly, if the object is moving downward, regardless of any other aspect of its motion, its y velocity is negative. Hint 2. Sketch Alex’s initial velocity On the diagram below, sketch the vector representing Alex’s velocity the instant after he leaves the ground at the beginning of the jump. ANSWER: ANSWER: Typesetting math: 100% Answer Requested Part B Determine the algebraic signs of Alex’s x velocity and y velocity the instant before he lands at the end of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Sketch Alex’s final velocity On the diagram below, sketch the vector representing Alex’s velocity the instant before he safely lands on the other side of the crevasse. ANSWER: Answer Requested ANSWER: Answer Requested Typesetting math: 100% At the buzzer, a basketball player shoots a desperation shot. The ball goes in! Part C Determine the algebraic signs of the ball’s x velocity and y velocity the instant after it leaves the player’s hands. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s initial velocity On the diagram below, sketch the vector representing the velocity of the basketball the instant after it leaves the player’s hands. ANSWER: Typesetting math: 100% ANSWER: Correct Part D Determine the algebraic signs of the ball’s x velocity and y velocity at the ball’s maximum height. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s velocity at maximum height Typesetting math: 100% On the diagram below, sketch the vector representing the velocity of the basketball the instant it reaches its maximum height. ANSWER: ANSWER: Answer Requested PSS 4.1 Projectile Motion Problems Learning Goal: Typesetting math: 100% To practice Problem-Solving Strategy 4.1 for projectile motion problems. A rock thrown with speed 9.00 and launch angle 30.0 (above the horizontal) travels a horizontal distance of = 17.0 before hitting the ground. From what height was the rock thrown? Use the value = 9.810 for the free-fall acceleration. PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems MODEL: Make simplifying assumptions, such as treating the object as a particle. Is it reasonable to ignore air resistance? VISUALIZE: Use a pictorial representation. Establish a coordinate system with the x axis horizontal and the y axis vertical. Show important points in the motion on a sketch. Define symbols, and identify what you are trying to find. SOLVE: The acceleration is known: and . Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are , . is the same for the horizontal and vertical components of the motion. Find from one component, and then use that value for the other component. ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model Start by making simplifying assumptions: Model the rock as a particle in free fall. You can ignore air resistance because the rock is a relatively heavy object moving relatively slowly. Visualize Part A Which diagram represents an accurate sketch of the rock’s trajectory? Hint 1. The launch angle In a projectile’s motion, the angle of the initial velocity above the horizontal is called the launch angle. ANSWER: m/s  d m g m/s2 ax = 0 ay = −g xf = xi +vixt, yf = yi +viyt− g(t 1 2 )2 vfx = vix = constant, and vfy = viy − gt t t v i Typesetting math: 100% Typesetting math: 100% Correct Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile’s acceleration, , is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn’t change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? ANSWER: ay At ground level below the point where the rock is launched At the point where the rock strikes the ground At the peak of the trajectory At the point where the rock is released At ground level below the peak of the trajectory Typesetting math: 100% Correct It’s best to place the origin of the coordinate system at ground level below the launching point because in this way all the points of interest (the launching point and the landing point) will have positive coordinates. (Based on your experience, you know that it’s generally easier to work with positive coordinates.) Keep in mind, however, that this is an arbitrary choice. The correct solution of the problem will not depend on the location of the origin of your coordinate system. Now, define symbols representing initial and final position, velocity, and time. Your target variable is , the initial y coordinate of the rock. Your pictorial representation should be complete now, and similar to the picture below: Solve Part C Find the height from which the rock was launched. Express your answer in meters to three significant figures. yi yi Typesetting math: 100% Hint 1. How to approach the problem The time needed to move horizontally to the final position = 17.0 is the same time needed for the rock to rise from the initial position to the peak of its trajectory and then fall to the ground. Use the information you have about motion in the horizontal direction to solve for . Knowing this time will allow you to use the equations of motion for the vertical direction to solve for . Hint 2. Find the time spent in the air How long ( ) is the rock in the air? Express your answer in seconds to three significant figures. Hint 1. Determine which equation to use Which of the equations given in the strategy and shown below is the most appropriate to calculate the time the rock spent in the air? ANSWER: Hint 2. Find the x component of the initial velocity What is the x component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: t xf = d m yi t yi t t xf = xi + vixt yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt vix = 7.79 m/s Typesetting math: 100% Hint 3. Find the y component of the initial velocity What is the y component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: Answer Requested Assess Part D A second rock is thrown straight upward with a speed 4.500 . If this rock takes 2.181 to fall to the ground, from what height was it released? Express your answer in meters to three significant figures. Hint 1. Identify the known variables What are the values of , , , and for the second rock? Take the positive y axis to be upward and the origin to be located on the ground where the rock lands. Express your answers to four significant figures in the units shown to the right, separated by commas. ANSWER: t = 2.18 s viy = 4.50 m/s yi = 13.5 m m/s s H yf viy t a Typesetting math: 100% Answer Requested Hint 2. Determine which equation to use to find the height Which equation should you use to find ? Keep in mind that if the positive y axis is upward and the origin is located on the ground, . ANSWER: ANSWER: Answer Requested Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction. Because both rocks were thrown with the same initial vertical velocity, 4.500 , and fell the same vertical distance of 13.5 , they were in the air for the same amount of time. This result was expected and helps to confirm that you did the calculation in Part C correctly. ± Arrow Hits Apple An arrow is shot at an angle of above the horizontal. The arrow hits a tree a horizontal distance away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity. Part A , , , = 0,4.500,2.181,-yf viy t a 9.810 m, m/s, s, m/s2 H yi = H yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt = − 2g( − ) v2f y v2i y yf yi H = 13.5 m viy = m/s m  = 45 D = 220 m g = 9.8 m/s2 Typesetting math: 100% Find , the time that the arrow spends in the air. Answer numerically in seconds, to two significant figures. Hint 1. Find the initial upward component of velocity in terms of D. Introduce the (unknown) variables and for the initial components of velocity. Then use kinematics to relate them and solve for . What is the vertical component of the initial velocity? Express your answer symbolically in terms of and . Hint 1. Find Find the horizontal component of the initial velocity. Express your answer symbolically in terms of and given symbolic quantities. ANSWER: Hint 2. Find What is the vertical component of the initial velocity? Express your answer symbolically in terms of . ANSWER: ANSWER: ta vy0 vx0 ta vy0 ta D vx0 vx0 ta vx0 = D ta vy0 vy0 vx0 vy0 = vx0 vy0 = D ta Typesetting math: 100% Hint 2. Find the time of flight in terms of the initial vertical component of velocity. From the change in the vertical component of velocity, you should be able to find in terms of and . Give your answer in terms of and . Hint 1. Find When applied to the y-component of velocity, in this problem the formula for with constant acceleration is What is , the vertical component of velocity when the arrow hits the tree? Answer symbolically in terms of only. ANSWER: ANSWER: Hint 3. Put the algebra together to find symbolically. If you have an expression for the initial vertical velocity component in terms in terms of and , and another in terms of and , you should be able to eliminate this initial component to find an expression for Express your answer symbolically in terms of given variables. ANSWER: ta vy0 g vy0 g vy(ta) v(t) −g vy(t) = vy0 − g t vy(ta ) vy0 vy(ta) = −vy0 ta = 2vy0 g ta D ta g ta ta2 t2 = a 2D g Typesetting math: 100% ANSWER: Answer Requested Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree. Part B How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Express your answer numerically in seconds, to two significant figures. Hint 1. When should the apple be dropped The apple should be dropped at the time equal to the total time it takes the arrow to reach the tree minus the time it takes the apple to fall 6.0 meters. Hint 2. Find the time it takes for the apple to fall 6.0 meters How long does it take an apple to fall 6.0 meters? Express your answer numerically in seconds, to two significant figures. ANSWER: Answer Requested ANSWER: ta = 6.7 s tf = 1.1 s td = 5.6 s Typesetting math: 100% Answer Requested Video Tutor: Ball Fired Upward from Accelerating Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Consider the video you just watched. Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment? Hint 1. Determine how long the ball is in the air How will doubling the initial upward speed of the ball change the time the ball spends in the air? A kinematic equation may be helpful here. The time in the air will ANSWER: be cut in half. stay the same. double. quadruple. Typesetting math: 100% Hint 2. Determine the appropriate kinematic expression Which of the following kinematic equations correctly describes the horizontal distance between the ball and the cart at the moment the ball lands? The cart’s initial horizontal velocity is , its horizontal acceleration is , and is the time elapsed between launch and impact. ANSWER: ANSWER: Correct The ball will spend twice as much time in the air ( , where is the ball’s initial upward velocity), so it will land four times farther behind the cart: (where is the cart’s horizontal acceleration). Video Tutor: Ball Fired Upward from Moving Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. d v0x ax t d = v0x t d = 1 2 axv0x t2 d = v0x t+ 1 2 axt2 d = 1 2 axt2 the same distance twice as far half as far four times as far by a factor not listed above t = 2v0y/g v0y d = 1 2 axt2 ax Typesetting math: 100% Part A The crew of a cargo plane wishes to drop a crate of supplies on a target below. To hit the target, when should the crew drop the crate? Ignore air resistance. Hint 1. How to approach the problem While the crate is on the plane, it shares the plane’s velocity. What is the crate’s velocity immediately after it is released? Hint 2. What affects the motion of the crate? Gravity will accelerate the crate downward. What, if anything, affects the crate’s horizontal motion? (Keep in mind that we are told to ignore air resistance, even though that’s not very realistic in this situation.) ANSWER: Correct At the moment it is released, the crate shares the plane’s horizontal velocity. In the absence of air resistance, the crate would remain directly below the plane as it fell. Score Summary: Your score on this assignment is 0%. Before the plane is directly over the target After the plane has flown over the target When the plane is directly over the target Typesetting math: 100% You received 0 out of a possible total of 0 points. Typesetting math: 100%

Chapter 4 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Advice for the Quarterback A quarterback is set up to throw the football to a receiver who is running with a constant velocity directly away from the quarterback and is now a distance away from the quarterback. The quarterback figures that the ball must be thrown at an angle to the horizontal and he estimates that the receiver must catch the ball a time interval after it is thrown to avoid having opposition players prevent the receiver from making the catch. In the following you may assume that the ball is thrown and caught at the same height above the level playing field. Assume that the y coordinate of the ball at the instant it is thrown or caught is and that the horizontal position of the quaterback is . Use for the magnitude of the acceleration due to gravity, and use the pictured inertial coordinate system when solving the problem. Part A Find , the vertical component of the velocity of the ball when the quarterback releases it. Express in terms of and . Hint 1. Equation of motion in y direction What is the expression for , the height of the ball as a function of time? Answer in terms of , , and . v r D  tc y = 0 x = 0 g v0y v0y tc g y(t) t g v0y ANSWER: Incorrect; Try Again Hint 2. Height at which the ball is caught, Remember that after time the ball was caught at the same height as it had been released. That is, . ANSWER: Answer Requested Part B Find , the initial horizontal component of velocity of the ball. Express your answer for in terms of , , and . Hint 1. Receiver’s position Find , the receiver’s position before he catches the ball. Answer in terms of , , and . ANSWER: Football’s position y(t) = v0yt− g 1 2 t2 y(tc) tc y(tc) = y0 = 0 v0y = gtc 2 v0x v0x D tc vr xr D vr tc xr = D + vrtc Typesetting math: 100% Find , the horizontal distance that the ball travels before reaching the receiver. Answer in terms of and . ANSWER: ANSWER: Answer Requested Part C Find the speed with which the quarterback must throw the ball. Answer in terms of , , , and . Hint 1. How to approach the problem Remember that velocity is a vector; from solving Parts A and B you have the two components, from which you can find the magnitude of this vector. ANSWER: Answer Requested Part D xc v0x tc xc = v0xtc v0x = + D tc vr v0 D tc vr g v0 = ( + ) + D tc vr 2 ( ) gtc 2 2 −−−−−−−−−−−−−−−−−−−  Typesetting math: 100% Assuming that the quarterback throws the ball with speed , find the angle above the horizontal at which he should throw it. Your solution should contain an inverse trig function (entered as asin, acos, or atan). Give your answer in terms of already known quantities, , , and . Hint 1. Find angle from and Think of velocity as a vector with Cartesian coordinates and . Find the angle that this vector would make with the x axis using the results of Parts A and B. ANSWER: Answer Requested Direction of Velocity at Various Times in Flight for Projectile Motion Conceptual Question For each of the motions described below, determine the algebraic sign (positive, negative, or zero) of the x component and y component of velocity of the object at the time specified. For all of the motions, the positive x axis points to the right and the positive y axis points upward. Alex, a mountaineer, must leap across a wide crevasse. The other side of the crevasse is below the point from which he leaps, as shown in the figure. Alex leaps horizontally and successfully makes the jump. v0  v0x v0y v0  v0x v0y v0xx^ v0yy^   = atan( ) v0y v0x Typesetting math: 100% Part A Determine the algebraic sign of Alex’s x velocity and y velocity at the instant he leaves the ground at the beginning of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Algebraic sign of velocity The algebraic sign of the velocity is determined solely by comparing the direction in which the object is moving with the direction that is defined to be positive. In this example, to the right is defined to be the positive x direction and upward the positive y direction. Therefore, any object moving to the right, whether speeding up, slowing down, or even simultaneously moving upward or downward, has a positive x velocity. Similarly, if the object is moving downward, regardless of any other aspect of its motion, its y velocity is negative. Hint 2. Sketch Alex’s initial velocity On the diagram below, sketch the vector representing Alex’s velocity the instant after he leaves the ground at the beginning of the jump. ANSWER: ANSWER: Typesetting math: 100% Answer Requested Part B Determine the algebraic signs of Alex’s x velocity and y velocity the instant before he lands at the end of the jump. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Typesetting math: 100% Hint 1. Sketch Alex’s final velocity On the diagram below, sketch the vector representing Alex’s velocity the instant before he safely lands on the other side of the crevasse. ANSWER: Answer Requested ANSWER: Answer Requested Typesetting math: 100% At the buzzer, a basketball player shoots a desperation shot. The ball goes in! Part C Determine the algebraic signs of the ball’s x velocity and y velocity the instant after it leaves the player’s hands. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s initial velocity On the diagram below, sketch the vector representing the velocity of the basketball the instant after it leaves the player’s hands. ANSWER: Typesetting math: 100% ANSWER: Correct Part D Determine the algebraic signs of the ball’s x velocity and y velocity at the ball’s maximum height. Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+). Hint 1. Sketch the basketball’s velocity at maximum height Typesetting math: 100% On the diagram below, sketch the vector representing the velocity of the basketball the instant it reaches its maximum height. ANSWER: ANSWER: Answer Requested PSS 4.1 Projectile Motion Problems Learning Goal: Typesetting math: 100% To practice Problem-Solving Strategy 4.1 for projectile motion problems. A rock thrown with speed 9.00 and launch angle 30.0 (above the horizontal) travels a horizontal distance of = 17.0 before hitting the ground. From what height was the rock thrown? Use the value = 9.810 for the free-fall acceleration. PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems MODEL: Make simplifying assumptions, such as treating the object as a particle. Is it reasonable to ignore air resistance? VISUALIZE: Use a pictorial representation. Establish a coordinate system with the x axis horizontal and the y axis vertical. Show important points in the motion on a sketch. Define symbols, and identify what you are trying to find. SOLVE: The acceleration is known: and . Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are , . is the same for the horizontal and vertical components of the motion. Find from one component, and then use that value for the other component. ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model Start by making simplifying assumptions: Model the rock as a particle in free fall. You can ignore air resistance because the rock is a relatively heavy object moving relatively slowly. Visualize Part A Which diagram represents an accurate sketch of the rock’s trajectory? Hint 1. The launch angle In a projectile’s motion, the angle of the initial velocity above the horizontal is called the launch angle. ANSWER: m/s  d m g m/s2 ax = 0 ay = −g xf = xi +vixt, yf = yi +viyt− g(t 1 2 )2 vfx = vix = constant, and vfy = viy − gt t t v i Typesetting math: 100% Typesetting math: 100% Correct Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile’s acceleration, , is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn’t change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? ANSWER: ay At ground level below the point where the rock is launched At the point where the rock strikes the ground At the peak of the trajectory At the point where the rock is released At ground level below the peak of the trajectory Typesetting math: 100% Correct It’s best to place the origin of the coordinate system at ground level below the launching point because in this way all the points of interest (the launching point and the landing point) will have positive coordinates. (Based on your experience, you know that it’s generally easier to work with positive coordinates.) Keep in mind, however, that this is an arbitrary choice. The correct solution of the problem will not depend on the location of the origin of your coordinate system. Now, define symbols representing initial and final position, velocity, and time. Your target variable is , the initial y coordinate of the rock. Your pictorial representation should be complete now, and similar to the picture below: Solve Part C Find the height from which the rock was launched. Express your answer in meters to three significant figures. yi yi Typesetting math: 100% Hint 1. How to approach the problem The time needed to move horizontally to the final position = 17.0 is the same time needed for the rock to rise from the initial position to the peak of its trajectory and then fall to the ground. Use the information you have about motion in the horizontal direction to solve for . Knowing this time will allow you to use the equations of motion for the vertical direction to solve for . Hint 2. Find the time spent in the air How long ( ) is the rock in the air? Express your answer in seconds to three significant figures. Hint 1. Determine which equation to use Which of the equations given in the strategy and shown below is the most appropriate to calculate the time the rock spent in the air? ANSWER: Hint 2. Find the x component of the initial velocity What is the x component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: t xf = d m yi t yi t t xf = xi + vixt yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt vix = 7.79 m/s Typesetting math: 100% Hint 3. Find the y component of the initial velocity What is the y component of the rock’s initial velocity? Express your answer in meters per second to three significant figures. ANSWER: ANSWER: Answer Requested Assess Part D A second rock is thrown straight upward with a speed 4.500 . If this rock takes 2.181 to fall to the ground, from what height was it released? Express your answer in meters to three significant figures. Hint 1. Identify the known variables What are the values of , , , and for the second rock? Take the positive y axis to be upward and the origin to be located on the ground where the rock lands. Express your answers to four significant figures in the units shown to the right, separated by commas. ANSWER: t = 2.18 s viy = 4.50 m/s yi = 13.5 m m/s s H yf viy t a Typesetting math: 100% Answer Requested Hint 2. Determine which equation to use to find the height Which equation should you use to find ? Keep in mind that if the positive y axis is upward and the origin is located on the ground, . ANSWER: ANSWER: Answer Requested Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction. Because both rocks were thrown with the same initial vertical velocity, 4.500 , and fell the same vertical distance of 13.5 , they were in the air for the same amount of time. This result was expected and helps to confirm that you did the calculation in Part C correctly. ± Arrow Hits Apple An arrow is shot at an angle of above the horizontal. The arrow hits a tree a horizontal distance away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity. Part A , , , = 0,4.500,2.181,-yf viy t a 9.810 m, m/s, s, m/s2 H yi = H yf = yi + viyt− g(t 1 2 )2 vfy = viy − gt = − 2g( − ) v2f y v2i y yf yi H = 13.5 m viy = m/s m  = 45 D = 220 m g = 9.8 m/s2 Typesetting math: 100% Find , the time that the arrow spends in the air. Answer numerically in seconds, to two significant figures. Hint 1. Find the initial upward component of velocity in terms of D. Introduce the (unknown) variables and for the initial components of velocity. Then use kinematics to relate them and solve for . What is the vertical component of the initial velocity? Express your answer symbolically in terms of and . Hint 1. Find Find the horizontal component of the initial velocity. Express your answer symbolically in terms of and given symbolic quantities. ANSWER: Hint 2. Find What is the vertical component of the initial velocity? Express your answer symbolically in terms of . ANSWER: ANSWER: ta vy0 vx0 ta vy0 ta D vx0 vx0 ta vx0 = D ta vy0 vy0 vx0 vy0 = vx0 vy0 = D ta Typesetting math: 100% Hint 2. Find the time of flight in terms of the initial vertical component of velocity. From the change in the vertical component of velocity, you should be able to find in terms of and . Give your answer in terms of and . Hint 1. Find When applied to the y-component of velocity, in this problem the formula for with constant acceleration is What is , the vertical component of velocity when the arrow hits the tree? Answer symbolically in terms of only. ANSWER: ANSWER: Hint 3. Put the algebra together to find symbolically. If you have an expression for the initial vertical velocity component in terms in terms of and , and another in terms of and , you should be able to eliminate this initial component to find an expression for Express your answer symbolically in terms of given variables. ANSWER: ta vy0 g vy0 g vy(ta) v(t) −g vy(t) = vy0 − g t vy(ta ) vy0 vy(ta) = −vy0 ta = 2vy0 g ta D ta g ta ta2 t2 = a 2D g Typesetting math: 100% ANSWER: Answer Requested Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree. Part B How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Express your answer numerically in seconds, to two significant figures. Hint 1. When should the apple be dropped The apple should be dropped at the time equal to the total time it takes the arrow to reach the tree minus the time it takes the apple to fall 6.0 meters. Hint 2. Find the time it takes for the apple to fall 6.0 meters How long does it take an apple to fall 6.0 meters? Express your answer numerically in seconds, to two significant figures. ANSWER: Answer Requested ANSWER: ta = 6.7 s tf = 1.1 s td = 5.6 s Typesetting math: 100% Answer Requested Video Tutor: Ball Fired Upward from Accelerating Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Consider the video you just watched. Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment? Hint 1. Determine how long the ball is in the air How will doubling the initial upward speed of the ball change the time the ball spends in the air? A kinematic equation may be helpful here. The time in the air will ANSWER: be cut in half. stay the same. double. quadruple. Typesetting math: 100% Hint 2. Determine the appropriate kinematic expression Which of the following kinematic equations correctly describes the horizontal distance between the ball and the cart at the moment the ball lands? The cart’s initial horizontal velocity is , its horizontal acceleration is , and is the time elapsed between launch and impact. ANSWER: ANSWER: Correct The ball will spend twice as much time in the air ( , where is the ball’s initial upward velocity), so it will land four times farther behind the cart: (where is the cart’s horizontal acceleration). Video Tutor: Ball Fired Upward from Moving Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. d v0x ax t d = v0x t d = 1 2 axv0x t2 d = v0x t+ 1 2 axt2 d = 1 2 axt2 the same distance twice as far half as far four times as far by a factor not listed above t = 2v0y/g v0y d = 1 2 axt2 ax Typesetting math: 100% Part A The crew of a cargo plane wishes to drop a crate of supplies on a target below. To hit the target, when should the crew drop the crate? Ignore air resistance. Hint 1. How to approach the problem While the crate is on the plane, it shares the plane’s velocity. What is the crate’s velocity immediately after it is released? Hint 2. What affects the motion of the crate? Gravity will accelerate the crate downward. What, if anything, affects the crate’s horizontal motion? (Keep in mind that we are told to ignore air resistance, even though that’s not very realistic in this situation.) ANSWER: Correct At the moment it is released, the crate shares the plane’s horizontal velocity. In the absence of air resistance, the crate would remain directly below the plane as it fell. Score Summary: Your score on this assignment is 0%. Before the plane is directly over the target After the plane has flown over the target When the plane is directly over the target Typesetting math: 100% You received 0 out of a possible total of 0 points. Typesetting math: 100%

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The bond length in an HCl molecule is 1.27 Å and the measured dipole moment is 1.08 D. What is the magnitude (in units of e) of the negative charge on Cl in HCl? (1 debye = 3.34 10 30 coulomb-meters − × ; e=1.6 10 19 coulombs − × ) A) 1.6 10 19 − × B) 0.057 C) 0.18 D) 1 E) 0.22

The bond length in an HCl molecule is 1.27 Å and the measured dipole moment is 1.08 D. What is the magnitude (in units of e) of the negative charge on Cl in HCl? (1 debye = 3.34 10 30 coulomb-meters − × ; e=1.6 10 19 coulombs − × ) A) 1.6 10 19 − × B) 0.057 C) 0.18 D) 1 E) 0.22

C) 0.18
For Day 12 and 13 Homework Cover Sheet Name:_________________________________________________ 1. Read Pages from 184-226, or watch the videos listed below  Properties of Subtraction http://www.youtube.com/watch?v=W9PEgpFyAYg (15 min)  Subtraction Algorithm http://www.youtube.com/watch?v=azaR-4ySSwQ (9 min) Visualizing Subtraction http://www.youtube.com/watch?v=PwQGc_1p0jQ (8 min)  Subtraction http://www.youtube.com/watch?v=E7Cj8QnEmNo (12 min)  Subtraction of Rational Expressions http://www.youtube.com/watch?v=Vuvmrq54b4w (8 min)  Prime factors and multiples of expressions http://www.youtube.com/watch?v=wy7pm8wjm_8 (8 min)  Multiples http://www.youtube.com/watch?v=f3ZdozzChjQ (9 min)  Least Common Multiples http://www.youtube.com/watch?v=wJCWNcytyXE (15 min)  Adding Rational Expressions Using LCM http://www.youtube.com/watch?v=O0V6hbTE-2s (12 min) 2. Attempt problems from workbook pages 51-66 Summary of the lectures you watched. List any parts of the video lecture (if there are any) that were unclear or you had trouble understanding. Please be specific and do not just say “All of it”. Questions you had difficulty with or felt stuck on- ALEKS Topics Mastered Word problem with powers of ten Combining like terms: Advanced Combining like terms: Integer coefficients Distributive property: Integer coefficients Elapsed time Estimating a decimal sum or difference Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 Integer subtraction: Problem type 3 Multiplication involving binomials and trinomials in two variables Multiplying a univariate polynomial by a monomial with a negative coefficient Multiplying binomials with negative coefficients Signed decimal addition and subtraction Signed decimal addition and subtraction with 3 numbers Signed fraction addition or subtraction: Basic Simplifying a sum or difference of multivariate polynomials Simplifying a sum or difference of three univariate polynomials Simplifying a sum or difference of two univariate polynomials Subtracting a 1-digit number from a 2-digit number Subtraction and regrouping with zeros Subtraction with borrowing Subtraction with multiple regrouping steps Subtraction without borrowing Word problem with addition or subtraction of whole numbers Adding or subtracting complex numbers

For Day 12 and 13 Homework Cover Sheet Name:_________________________________________________ 1. Read Pages from 184-226, or watch the videos listed below  Properties of Subtraction http://www.youtube.com/watch?v=W9PEgpFyAYg (15 min)  Subtraction Algorithm http://www.youtube.com/watch?v=azaR-4ySSwQ (9 min) Visualizing Subtraction http://www.youtube.com/watch?v=PwQGc_1p0jQ (8 min)  Subtraction http://www.youtube.com/watch?v=E7Cj8QnEmNo (12 min)  Subtraction of Rational Expressions http://www.youtube.com/watch?v=Vuvmrq54b4w (8 min)  Prime factors and multiples of expressions http://www.youtube.com/watch?v=wy7pm8wjm_8 (8 min)  Multiples http://www.youtube.com/watch?v=f3ZdozzChjQ (9 min)  Least Common Multiples http://www.youtube.com/watch?v=wJCWNcytyXE (15 min)  Adding Rational Expressions Using LCM http://www.youtube.com/watch?v=O0V6hbTE-2s (12 min) 2. Attempt problems from workbook pages 51-66 Summary of the lectures you watched. List any parts of the video lecture (if there are any) that were unclear or you had trouble understanding. Please be specific and do not just say “All of it”. Questions you had difficulty with or felt stuck on- ALEKS Topics Mastered Word problem with powers of ten Combining like terms: Advanced Combining like terms: Integer coefficients Distributive property: Integer coefficients Elapsed time Estimating a decimal sum or difference Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 Integer subtraction: Problem type 3 Multiplication involving binomials and trinomials in two variables Multiplying a univariate polynomial by a monomial with a negative coefficient Multiplying binomials with negative coefficients Signed decimal addition and subtraction Signed decimal addition and subtraction with 3 numbers Signed fraction addition or subtraction: Basic Simplifying a sum or difference of multivariate polynomials Simplifying a sum or difference of three univariate polynomials Simplifying a sum or difference of two univariate polynomials Subtracting a 1-digit number from a 2-digit number Subtraction and regrouping with zeros Subtraction with borrowing Subtraction with multiple regrouping steps Subtraction without borrowing Word problem with addition or subtraction of whole numbers Adding or subtracting complex numbers

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Southwest Rafters Case 2:Case 1: Capital Budgeting Cash Flows and Capital Budgeting Techniques Create a data sheet (or section) and link calculations to the data so that if the data is updated the calculations automatically update. 1) Calculate the Initial Cash Outlay and Annual Capital Budgeting Cash Flow for years 1 thru 5 for both alternatives. 2) Discuss the ethical implications of this business. Might there be a difference between these two alternatives? 3) Calculate the Payback Period, Net Present Value and Internal Rate of Return for both alternatives based on your Initial Cash Outlay and Capital Budgeting Cash Flows. 4) Calculate NPV and IRR if cash flows increase at an estimated 6% annual rate. 5) What discount rate would leave them indifferent between the two alternatives? 6) What does the discount rate in #5 imply about the growth rate needed to make the Buenaventura better than the Green? 7) What is the probability of negative NPV both in the case of perfect serial correlation and in the case of independence of cash flows for both alternatives? Assume no growth and a $5,000 standard deviation of annual cash flow for both alternatives. 8) Calculate Accounting (Profit) and Cash Breakeven Points (average number of clients per trip) and the Degree of Operating Leverage for both alternatives for year 1. Treat all revenue as variable. Treat all expenses as fixed except the client portion of transportation and food and the administrative cost. Include externalities. If you spreadsheet is functional BEP is easy! 9) Could either alternative have Multiple Internal Rates of Return? Explain 10) Discuss the option values associated with these alternatives. Is there a difference between them? 11) Which alternative do you recommend for Southwest Rafters? Defend your choice using the results from the other questions. Assume that the assumptions are reasonable.

Southwest Rafters Case 2:Case 1: Capital Budgeting Cash Flows and Capital Budgeting Techniques Create a data sheet (or section) and link calculations to the data so that if the data is updated the calculations automatically update. 1) Calculate the Initial Cash Outlay and Annual Capital Budgeting Cash Flow for years 1 thru 5 for both alternatives. 2) Discuss the ethical implications of this business. Might there be a difference between these two alternatives? 3) Calculate the Payback Period, Net Present Value and Internal Rate of Return for both alternatives based on your Initial Cash Outlay and Capital Budgeting Cash Flows. 4) Calculate NPV and IRR if cash flows increase at an estimated 6% annual rate. 5) What discount rate would leave them indifferent between the two alternatives? 6) What does the discount rate in #5 imply about the growth rate needed to make the Buenaventura better than the Green? 7) What is the probability of negative NPV both in the case of perfect serial correlation and in the case of independence of cash flows for both alternatives? Assume no growth and a $5,000 standard deviation of annual cash flow for both alternatives. 8) Calculate Accounting (Profit) and Cash Breakeven Points (average number of clients per trip) and the Degree of Operating Leverage for both alternatives for year 1. Treat all revenue as variable. Treat all expenses as fixed except the client portion of transportation and food and the administrative cost. Include externalities. If you spreadsheet is functional BEP is easy! 9) Could either alternative have Multiple Internal Rates of Return? Explain 10) Discuss the option values associated with these alternatives. Is there a difference between them? 11) Which alternative do you recommend for Southwest Rafters? Defend your choice using the results from the other questions. Assume that the assumptions are reasonable.

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PHET ElectroMagnetism Key to this Document Instructions are in black. Experimental questions that you need to solve through experimentation with an online animation are in green highlighted. Important instructions are in red highlighted. Items that need a response from you are in yellow highlighted. Please put your answers to this activity in RED. Part I- Comparing Permanent Magnets and Electromagnets: 1. Select the simulation “Magnets and Electromagnets.” It is at this link: http://phet.colorado.edu/new/simulations/sims.php?sim=Magnets_and_Electromagnets 2. Move the compass slowly along a semicircular path above the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 3. Move the compass along a semicircular path below the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 4. What do you suppose the compass needles drawn all over the screen tell you? 5. Use page 10 in your book to look up what it looks like when scientists use a drawing to represent a magnetic field. Describe the field around a bar magnet here. 6. Put the compass to the left or right of the magnet. Click “flip polarity” and notice what happens to the compass. Using the compass needle as your observation tool, describe the effect that flipping the poles of the magnet has on the magnetic field. 7. Click on the electromagnet tab along the top of the simulation window. Place the compass on the left side of the coil so that the compass center lies along the axis of the coil. <--like this 8. Move the compass along a semicircular path above the coil until you’ve put it on the opposite side of the coil. Then do the same below the coil. Notice what happens to the compass needle. Compare this answer to the answer you got to Number 2 and 3. 9. Compare the shape of the magnetic field of a bar magnet to the magnetic field of an electromagnet. 10. Use the voltage slider to change the direction of the current and investigate the shape of the magnetic field the coil using the compass after you’ve let the compass stabilize. Summarize, the effect that the direction of current has on the shape of the magnetic field around an electrified coil of wires. 11. What happens to the current in the coil when you set the voltage of the battery to zero? 12. What happens to the magnetic field around the coil when you set the voltage of the battery to zero? Part II – Investigating relationships- No Answers are written on this document after this point. All three data tables, graphs and conclusion statements go on the Google Spreadsheet that you can download from Ms. Pogge’s website. Experimental Question #1: How does distance affect the strength of the magnetic field around an electromagnet? 1. Using the Electromagnet simulation, click on “Show Field Meter.” 2. Set the battery voltage to 10V where the positive is on the right of the battery (slide the switch all the way to the right). 3. Magnetic field strength (symbol B on the top line of the meter) is measured in gauss (G). You’ll only need to record the value on the top line of the Field Meter. 4. Position zero will be right on top of the coil. Negative number positions will be to the left and positive number positions to the right of the coil. 5. Move the field meter one compass needle to the right and record the value of B at position 1. 6. This data table below will be used to help you fill in the first spreadsheet you downloaded from Ms. Pogge’s website. You will end up with 3 data tables, 3 graphs and 3 conclusion statements in your document, one for each mini-experiment you are doing. a. NOTE: Be sure to take all of your values along the horizontal axis of the coil. You’ll know you’re on the axis because the B-y measurement of the magnetic field is zero along the axis. Compass position (no units) Magnetic Field Strength ( )<--Fill in units! -5 (5 needles to the left of coil) Don’t fill in the table here...do it on the Google Spreadsheet you downloaded -4 -3 -2 -1 0 (middle of coil) 1 2 3 4 5 (5 needles to right of coil) 7. In your Google Spreadsheet: Graph the compass position on the horizontal (x) axis and magnetic field magnitude on the vertical (y) axis. 8. Make sure to label the axes and title the graph. Share this spreadsheet with your teacher. 9. Analyze your graph to discover how the two variables are related, and report the relationship between magnetic field strength and position using 1-3 complete sentences. Experimental Question #2: How does the number of coils affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the number of coils. Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet. Experimental Question #3: How does the amount of current affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the Current. (Recall that voltage is directly proportional to current….Ohm’s Law.) Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet.

PHET ElectroMagnetism Key to this Document Instructions are in black. Experimental questions that you need to solve through experimentation with an online animation are in green highlighted. Important instructions are in red highlighted. Items that need a response from you are in yellow highlighted. Please put your answers to this activity in RED. Part I- Comparing Permanent Magnets and Electromagnets: 1. Select the simulation “Magnets and Electromagnets.” It is at this link: http://phet.colorado.edu/new/simulations/sims.php?sim=Magnets_and_Electromagnets 2. Move the compass slowly along a semicircular path above the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 3. Move the compass along a semicircular path below the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 4. What do you suppose the compass needles drawn all over the screen tell you? 5. Use page 10 in your book to look up what it looks like when scientists use a drawing to represent a magnetic field. Describe the field around a bar magnet here. 6. Put the compass to the left or right of the magnet. Click “flip polarity” and notice what happens to the compass. Using the compass needle as your observation tool, describe the effect that flipping the poles of the magnet has on the magnetic field. 7. Click on the electromagnet tab along the top of the simulation window. Place the compass on the left side of the coil so that the compass center lies along the axis of the coil. <--like this 8. Move the compass along a semicircular path above the coil until you’ve put it on the opposite side of the coil. Then do the same below the coil. Notice what happens to the compass needle. Compare this answer to the answer you got to Number 2 and 3. 9. Compare the shape of the magnetic field of a bar magnet to the magnetic field of an electromagnet. 10. Use the voltage slider to change the direction of the current and investigate the shape of the magnetic field the coil using the compass after you’ve let the compass stabilize. Summarize, the effect that the direction of current has on the shape of the magnetic field around an electrified coil of wires. 11. What happens to the current in the coil when you set the voltage of the battery to zero? 12. What happens to the magnetic field around the coil when you set the voltage of the battery to zero? Part II – Investigating relationships- No Answers are written on this document after this point. All three data tables, graphs and conclusion statements go on the Google Spreadsheet that you can download from Ms. Pogge’s website. Experimental Question #1: How does distance affect the strength of the magnetic field around an electromagnet? 1. Using the Electromagnet simulation, click on “Show Field Meter.” 2. Set the battery voltage to 10V where the positive is on the right of the battery (slide the switch all the way to the right). 3. Magnetic field strength (symbol B on the top line of the meter) is measured in gauss (G). You’ll only need to record the value on the top line of the Field Meter. 4. Position zero will be right on top of the coil. Negative number positions will be to the left and positive number positions to the right of the coil. 5. Move the field meter one compass needle to the right and record the value of B at position 1. 6. This data table below will be used to help you fill in the first spreadsheet you downloaded from Ms. Pogge’s website. You will end up with 3 data tables, 3 graphs and 3 conclusion statements in your document, one for each mini-experiment you are doing. a. NOTE: Be sure to take all of your values along the horizontal axis of the coil. You’ll know you’re on the axis because the B-y measurement of the magnetic field is zero along the axis. Compass position (no units) Magnetic Field Strength ( )<--Fill in units! -5 (5 needles to the left of coil) Don’t fill in the table here...do it on the Google Spreadsheet you downloaded -4 -3 -2 -1 0 (middle of coil) 1 2 3 4 5 (5 needles to right of coil) 7. In your Google Spreadsheet: Graph the compass position on the horizontal (x) axis and magnetic field magnitude on the vertical (y) axis. 8. Make sure to label the axes and title the graph. Share this spreadsheet with your teacher. 9. Analyze your graph to discover how the two variables are related, and report the relationship between magnetic field strength and position using 1-3 complete sentences. Experimental Question #2: How does the number of coils affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the number of coils. Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet. Experimental Question #3: How does the amount of current affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the Current. (Recall that voltage is directly proportional to current….Ohm’s Law.) Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet.

salt water contains n sodium ions (Na+) per cubic meter and n chloride ions (cI-) per cubic meter. A battery is connected to metal. A battery is connected to metal rods that dip into a narrow pipe full of the salt water. the cross sectional area of the pipe is A what is the direction of conventional current flow in the salt water? 1. to the right, 2. to the left, 3. there is no conventional current because the motion of the positive and negative ions cancel each other out.

salt water contains n sodium ions (Na+) per cubic meter and n chloride ions (cI-) per cubic meter. A battery is connected to metal. A battery is connected to metal rods that dip into a narrow pipe full of the salt water. the cross sectional area of the pipe is A what is the direction of conventional current flow in the salt water? 1. to the right, 2. to the left, 3. there is no conventional current because the motion of the positive and negative ions cancel each other out.

answer 2
Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and 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 , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x ANSWER: Answer Requested Part B What is the sign of the y component of vector 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, and , of vector shown in the figure. |Ax| = 5 m Ay A positive negative Bx By B Express your answers, separated by a comma, in meters to one significant figure. ANSWER: Correct Vector Components–Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and the coordinate axes, often designated . Bx, By = -2,-5 m, m F  Fx Fy  Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER:  Fx Fy F  Fx, Fy = Fcos, Fsin Correct In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies. Part B When you resolve a vector into components, the components must have the form or . The signs depend on which quadrant the vector lies in, and there will be one component with and the other with . In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you must figure out which angle is and then properly reorient the definitional triangle. As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle between and the y axis. Which of the various ways of orienting the definitional triangle must be used to resolve into components in the tilted coordinate system shown? (In the figures, the hypotenuse is orange, the side adjacent to is red, and the side opposite is yellow.) F  /2 cos() sin() F  sin(180 + ) = −sin() cos(90 + ) = −sin() sin() cos() sin(180 + ) + cos(270 − ) = 0 sin() cos()  /2 F  |F| cos() |F| sin() sin() cos()  N  N N  Indicate the number of the figure with the correct orientation. Hint 1. Recommended procedure for resolving a vector into components First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and write in the signs. Hint 2. Finding the trigonometric functions Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the   cos() side opposite has length . The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector whose magnitude is the hypotenuse; red + yellow = orange. ANSWER: Correct Part C Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: ANSWER: sin() 1 2 3 4 Correct Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates . Consider the following conditions: A. , B. , C. , D. , Which of these lettered conditions are true in which the numbered quadrants shown in ? Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and D in the fourth, enter “3, 2, 1, 4” as your response. ANSWER: Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle.     x > 0 y > 0 x > 0 y < 0 x < 0 y > 0 x < 0 y < 0 Correct Part E Now find the components and of in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Answer Requested ± 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. Nx Ny N N  Nx, Ny = −Nsin(),Ncos() T  T  Part A Find the components of the vector with length = 1.00 and angle =10.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. What is the x component? Look at the figure shown. points in the positive x direction, so is positive. Also, the magnitude is just the length . ANSWER: Correct Part B Find the components of the vector with length = 1.00 and angle =15.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. A a  A x Ax |Ax| OL = OMcos( ) A  = 0.985,0.174 B b   Hint 1. What is the x component? The x component is still of the same form, that is, . ANSWER: Correct The components of still have the same form, that is, , despite 's placement with respect to the y axis on the drawing. Part C Find the components of the vector with length = 1.00 and angle 35.0 as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. Method 1: Find the angle that makes with the positive x axis Angle = 0.611 differs from the other two angles because it is the angle between the vector and the y axis, unlike the others, which are with respect to the x axis. What is the angle that makes with the positive x axis? Express your answer numerically in degrees. ANSWER: Hint 2. Method 2: Use vector addition Look at the figure shown. Lcos() B = 0.966,0.259 B (Lcos(), Lsin()) B C c  =  C  C 125 1. . 2. . 3. , the x component of is negative, since points in the negative x direction. Use this information to find . Similarly, find . ANSWER: Answer Requested ± Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: Correct C = C + x C y |C | = length(QR) = c sin() x Cx C C x Cx Cy C  = -0.574,0.819 A = (1, 0,−3) B = (−2, 5, 1) C = (3, 1, 1) A − B  = 3,-5,-4 Part B ANSWER: Correct Part C ANSWER: Correct Part D ANSWER: Correct B − C  = -5,4,0 −A + B − C  = -6,4,3 3A − 2C  = -3,-2,-11 Part E ANSWER: Correct Part F ANSWER: Correct Video Tutor: Balls Take High and Low Tracks First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A −2A + 3B − C  = -11,14,8 2A − 3(B − C) = 17,-12,-6 Consider the video demonstration that you just watched. Which of the following changes could potentially allow the ball on the straight inclined (yellow) track to win? Ignore air resistance. Select all that apply. Hint 1. How to approach the problem Answers A and B involve changing the steepness of part or all of the track. Answers C and D involve changing the mass of the balls. So, first you should decide which of those factors, if either, can change how fast the ball gets to the end of the track. ANSWER: Correct If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt? Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. A. Increase the tilt of the yellow track. B. Make the downhill and uphill inclines on the red track less steep, while keeping the total distance traveled by the ball the same. C. Increase the mass of the ball on the yellow track. D. Decrease the mass of the ball on the red track.

Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and 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 , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x ANSWER: Answer Requested Part B What is the sign of the y component of vector 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, and , of vector shown in the figure. |Ax| = 5 m Ay A positive negative Bx By B Express your answers, separated by a comma, in meters to one significant figure. ANSWER: Correct Vector Components–Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and the coordinate axes, often designated . Bx, By = -2,-5 m, m F  Fx Fy  Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER:  Fx Fy F  Fx, Fy = Fcos, Fsin Correct In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies. Part B When you resolve a vector into components, the components must have the form or . The signs depend on which quadrant the vector lies in, and there will be one component with and the other with . In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you must figure out which angle is and then properly reorient the definitional triangle. As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle between and the y axis. Which of the various ways of orienting the definitional triangle must be used to resolve into components in the tilted coordinate system shown? (In the figures, the hypotenuse is orange, the side adjacent to is red, and the side opposite is yellow.) F  /2 cos() sin() F  sin(180 + ) = −sin() cos(90 + ) = −sin() sin() cos() sin(180 + ) + cos(270 − ) = 0 sin() cos()  /2 F  |F| cos() |F| sin() sin() cos()  N  N N  Indicate the number of the figure with the correct orientation. Hint 1. Recommended procedure for resolving a vector into components First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and write in the signs. Hint 2. Finding the trigonometric functions Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the   cos() side opposite has length . The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector whose magnitude is the hypotenuse; red + yellow = orange. ANSWER: Correct Part C Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: ANSWER: sin() 1 2 3 4 Correct Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates . Consider the following conditions: A. , B. , C. , D. , Which of these lettered conditions are true in which the numbered quadrants shown in ? Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and D in the fourth, enter “3, 2, 1, 4” as your response. ANSWER: Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle.     x > 0 y > 0 x > 0 y < 0 x < 0 y > 0 x < 0 y < 0 Correct Part E Now find the components and of in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Answer Requested ± 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. Nx Ny N N  Nx, Ny = −Nsin(),Ncos() T  T  Part A Find the components of the vector with length = 1.00 and angle =10.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. What is the x component? Look at the figure shown. points in the positive x direction, so is positive. Also, the magnitude is just the length . ANSWER: Correct Part B Find the components of the vector with length = 1.00 and angle =15.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. A a  A x Ax |Ax| OL = OMcos( ) A  = 0.985,0.174 B b   Hint 1. What is the x component? The x component is still of the same form, that is, . ANSWER: Correct The components of still have the same form, that is, , despite 's placement with respect to the y axis on the drawing. Part C Find the components of the vector with length = 1.00 and angle 35.0 as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. Method 1: Find the angle that makes with the positive x axis Angle = 0.611 differs from the other two angles because it is the angle between the vector and the y axis, unlike the others, which are with respect to the x axis. What is the angle that makes with the positive x axis? Express your answer numerically in degrees. ANSWER: Hint 2. Method 2: Use vector addition Look at the figure shown. Lcos() B = 0.966,0.259 B (Lcos(), Lsin()) B C c  =  C  C 125 1. . 2. . 3. , the x component of is negative, since points in the negative x direction. Use this information to find . Similarly, find . ANSWER: Answer Requested ± Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: Correct C = C + x C y |C | = length(QR) = c sin() x Cx C C x Cx Cy C  = -0.574,0.819 A = (1, 0,−3) B = (−2, 5, 1) C = (3, 1, 1) A − B  = 3,-5,-4 Part B ANSWER: Correct Part C ANSWER: Correct Part D ANSWER: Correct B − C  = -5,4,0 −A + B − C  = -6,4,3 3A − 2C  = -3,-2,-11 Part E ANSWER: Correct Part F ANSWER: Correct Video Tutor: Balls Take High and Low Tracks First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A −2A + 3B − C  = -11,14,8 2A − 3(B − C) = 17,-12,-6 Consider the video demonstration that you just watched. Which of the following changes could potentially allow the ball on the straight inclined (yellow) track to win? Ignore air resistance. Select all that apply. Hint 1. How to approach the problem Answers A and B involve changing the steepness of part or all of the track. Answers C and D involve changing the mass of the balls. So, first you should decide which of those factors, if either, can change how fast the ball gets to the end of the track. ANSWER: Correct If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt? Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. A. Increase the tilt of the yellow track. B. Make the downhill and uphill inclines on the red track less steep, while keeping the total distance traveled by the ball the same. C. Increase the mass of the ball on the yellow track. D. Decrease the mass of the ball on the red track.

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