Section 3-1 Constructing Complex Motions from Simple Motion *1. In Figure 3-1, the motion of a spinning wheel (W) that itself revolves in a circle is shown. Which of the following would not be represented by this type of motion? a. A planet in orbit around the sun b. A ride at an amusement park c. A wheel rolling on another wheel d. A car going around a race track e. The extended hand of a figure skater Figure 3-1 *2. A hoop rolls along a horizontal plane at a constant speed. Imagine a point on the hoop. Viewed from the side the components of its motion could best be described as: a. A circle upon a circle b. Two concentric circles c. A circle and a straight line d. A saw tooth on a straight line e. Two perpendicular straight lines 3. Two balls begin their motion simultaneously from the same height. One ball is simply dropped; the other is thrown horizontally. Which is not true? Neglect air resistance. a. The balls strike the ground with the same speed. b. The balls strike the ground at the same time. c. The acceleration is the same for both balls. d. Their vertical shadows look identical. e. The y-component of each ball s velocity is the same. 22
Section 3-2 Breaking Down Two-Dimensional Motions into One-Dimensional Components: Projectile Motion *4. A child swings a ball on a string in a circular motion. The ball moves in a plane vertical to the ground. If the sun is directly overhead how does the shadow move? a. In a circle b. In an ellipse c. In a figure 8 pattern d. In a straight line with constant velocity e. Back and forth along a straight line *5. A ball is thrown horizontally. How does its shadow on the ground compare to its vertical shadow? a. As the vertical shadow speeds up the horizontal shadow slows down. b. The vertical shadow speeds up; the horizontal shadow moves with uniform speed. c. The horizontal shadow speeds up; the vertical shadow moves with uniform speed. d. Both shadows speed up. e. Both shadows move with uniform speed. Section 3-3 Vectors 6. Which of the following is not descriptive of vectors? a. Length b. Resultant c. Magnitude d. Component e. Direction 7. The choice of coordinate axes for a given two-dimensional reference frame must a. always correspond to the vertical and horizontal direction. b. always represent position. c. always be perpendicular. d. always have the origin at zero. e. always correspond to the direction of the earth. 23
8. Vectors A v and B v both have a magnitude of 8. If their resultant has a magnitude of 10, what is the angle between them? a. 26 o b. 47 o c. 77 o d. 90 o e. 110 o 9. Two vectors can be added to produce resultants with magnitudes of 25 and 5. Which of the following pairs of vector magnitudes could not produce both of these resultants? a. A = 10, B = 15 b. A = 15, B = 10 c. A = 20, B = 15 d. A = 50, B = 50 e. A = 20, B = 10 10. Two vectors in one dimension have magnitudes A = 10.0 m, B = 5.0 m. Which is not a possible resultant of the two vectors? a. 5.0 m b. -5.0 m c. -15.0 m d. 15.0 m e. 1.5 m 11. Which is not true: The choice of coordinate frames a. does not affect the resultant vectors. b. can be chosen to simplify the problem. c. must conform to map coordinates. d. has two perpendicular axes. e. has an arbitrary origin. 24
*12. As measured from the +x-axis, vector A v makes an angle of 28 o. What angle does A v make with the y-axis? a. 180 o b. 152 o c. 90 o d. 62 o e. 28 o Section 3.4 Working with Vector Components Figure 3-2 v v 13. In Figure 3-2 if A= B, then a. A v = 93.4 m b. A v = 41.3 m c. A v = 37.7 m d. A v = 35.0 m e. A v = 14.1 m 14. In Figure 3-2 if a. A y = 46.7 m b. A y = 20.1 m c. A y = 18.9 m d. A y = 17.5 m e. A y = 7.1 m v A = 1 2 v B, then 25
15. All of the following paths start at the same point. Find the path that does not end where the others do. a. 10 m North, 5 m South, 3 m West, 4 m East b. 5 m North, 8 m East, 7 m West c. 8 m South, 3 m East, 13 m North, 2 m West d. 10 m North, 5 m West, 5 m South, 2 m East e. 15 m North, 8 m West, 9 m East, 10 m South 16. The components of a vector are 2.3m and 6.7 m. What is the magnitude of the vector? a. 2.3 m b. 4.4 m c. 6.3 m d. 7.1 m e. 9.0 m 17. A vector has magnitude of 10.0 and makes an angle of 125.0 o counterclockwise to the +x-axis. Its x- and y-components, respectively, are a. -8.2, -5.7 b. 8.2, -5.7 c. -5.7, 8.2 d. -5.7, -8.2 e. -7.1, 7.1 *18. A hiker sets out to travel 1.50 km 45 o northwest from her original position. She hikes 2.00 km directly west. What are the components of the vector that will take her from there to her destination? a. x = +0.94 km, y = +1.06 km b. x = -0.94 km, y = 1.06 km c. x= +2.0 km, y = +0.5 km d. x = -1.0 km, y = +0.5 km e. x = 0 km, y = +1.5 km 26
19. Find the magnitude and direction of an object with v x = 2.0 cm/s and v y = 3.0 cm/s. a. 3.6 cm/s, 34 o from the +x-axis b. 5.0 cm/s, 34 o from the +x-axis c. 3.6 cm/s, 56 o from the +x-axis d. 5.0 cm/s, 66 o from the +x-axis e. 3.6 cm/s, 66 o from the +x-axis *20. A vector has magnitude 12.7. Rounding off, which pair of components could not produce this vector? a. 12.2, 3.5 b. 10.2, 5.5 c. 9.6, 8.2 d. 7.1, 10.5 e. 6.3, 11.0 21. V x = 3.70 and V y = 8.40. Which is not true? a. V = 9.18 b. cos θ = 0.40 c. sin θ = 0.92 d. tan θ = 0.44 e. θ = 66.22 o 22. A v = 10.0 @ 30 o above the +x-axis and B v = 12.0 @ 60 o above the +x-axis. What is the magnitude of A v + B v? a. 22.0 b. 21.3 c. 15.4 d. 12.2 e. 10.0 23. A v = 10.0 @ 30 o above the +x-axis and B v = 12.0 @ 60 o above the +x-axis. What is the magnitude of A v B v? a. 2.0 b. 3.0 c. 4.0 d. 5.0 e. 6.0 27
24. A v = 10.0 @ 30 o above the +x-axis; B v = 12.0 @ 60 o above the +x-axis; and C v = 15.0 @ 50 o below the x-axis. What is the magnitude of A v + B v + C v? a. 6.1 b. 6.4 c. 8.6 d. 24.6 e. 37.0 *25. A v = 10.0 @ 30 o above the +x-axis; B v = 12.0 @ 60 o above the +x-axis; and C v = 15.0 @ 50 o below the x-axis. What is the magnitude of A v + B v C v? a. 36.2 b. 27.3 c. 19.0 d. 6.4 e. 4.4 26. A v = 10.0 @ 30 o above the +x-axis and B v = 12.0 @ 60 o above the +x-axis. What angle does A v + B v make with the +x-axis? a. 125.9 o b. 80.8 o c. 54.1 d. 46.4 o e. 0 *27. A v = 10.0 @ 30 o above the +x-axis; B v = 12.0 @ 60 o above the +x-axis; and C v = 15.0 @ 50 o below the x-axis. What angle does A v + B v + C v make with the +x-axis? a. 127.7 o b. 52.3 o c. 37.7 o d. 9.1 o e. 0 o 28
Section 3-5 Velocity and Acceleration Vectors 28. A car travels due East for 30.0 km and then due South for 45.0 km. This trip takes 3.5 hr. What is the magnitude of the car s average velocity? a. 15.5 km/hr b. 18.0 km/hr c. 21.4 km/hr d. 54.1 km/hr e. 75.0 km/hr 29. A turtle s velocity changes from v 1 = 1.0 mm/s at θ = 0.0 o to v 2 = 1.2 mm/s at θ = 20.0 o. What is the change in the turtle s velocity? Give your answer in component form (Δv x, Δv y ). a. Δv x = 0.2 mm/s Δv y = 0 b. Δv x = 0 Δv y = 0.2 mm/s c. Δv x = 0.4 mm/s Δv y = 0.1 mm/s d. Δv x = 0.1 mm/s Δv y = 0.4 mm/s e. Δv x = 0.1 mm/s Δv y = 0.1 mm/s *30. A bicyclist traveling at 10.0 m/s slows down to turn a corner. After completing the turn the bicyclist then has a speed of 7.0 m/s at an angle of 90.0 o to the original direction. If it takes 7.0 s to complete the turn what is the magnitude of the bicyclist s acceleration? a. 1.7 m/s 2 b. -1.7 m/s 2 c. 0.4 m/s 2 d. -3.0 m/s 2 e. 3.0 m/s 2 31. In Figure 3-3 the stopwatches measure seconds and Δr is 60 m. What is magnitude of the change in velocity of the race car? a. 20 m/s b. 30 m/s c. 40 m/s d. 50 m/s e. 60 m/s 29
Figure 3-3 *32. A race car rounds a curve in the track as shown in Figure 3-3. Which cannot be ascertained? a. The race car has accelerated. b. The direction of the race car has changed. c. The velocity of the race car has changed. d. The speed of the race car has changed. e. The displacement of the race car has changed. *33. In Figure 3-3, if r 0 is 50 m, r is 90 m, t 0 1.0 s, and t is 4.0 s, and the angle between r v and r v o is 25 o, what is the magnitude of the average velocity during this time of the race car? a. 73.0 m/s b. 46.7 m/s c. 16.5 m/s d. 13.3 m/s e. 12.4 m/s **34. A jogger maintains a constant speed around the boundaries of a rectangular field. Which of the following statements is true? a. The acceleration of the jogger is zero. b. The acceleration of the jogger is uniform. c. The acceleration of the jogger is sometimes zero. d. The acceleration of the jogger is sometimes uniform. e. The acceleration of the jogger is never zero. 30
Section 3-6 Solving Motion Problems in Two Dimensions: Projectile Motion Revisited Figure 3-4 35. In Figure 3-4 a typical path for projectile motion is shown. As the object descends, which pair of velocity and acceleration vectors might describe the motion of the object at any given instant? a. A b. B c. C d. D e. None of the above. 36. A projectile is launched with an initial speed of 50.0 m/s at an angle of 35.0 o. After 3.0 s, what is the magnitude of the x-component of its velocity? Neglect air resistance. a. 11.6 m/s b. 41.0 m/s c. 50.0 m/s d. 62.8 m/s e. 70.4 m/s *37. A child stands 3.0 m from a fence. The child throws a ball that just makes it over the fence at the top of its trajectory. If the child threw the ball with an initial speed of 10.0 m/s from a height of 1.3 m and at an angle of 70.0 o with respect to the vertical, how tall is the fence? a. 5.8 m b. 4.5 m c. 1.9 m d. 1.3 m e. 0.6 m 31
**38. A ball is thrown towards a 6.00 m distant wall from a height of 2.00 m. Its initial velocity is 15.0 m/s at an angle of 30.0 o to the horizontal. Find how far below the ball actually hits the wall compared to where it would have hit without any gravity. a. 6.00 m b. 3.46 m c. 2.42 m d. 2.00 m e. 1.04 m Figure 3-5 **39. A marksman aims a rifle to hit the bull s-eye of a target as shown in Figure 3-5. If θ = 1.5 o, and the bullet hits directly target center, what was the initial speed of the bullet? a. 130 m/s b. 170 m/s c. 240 m/s d. 370 m/s e. 560 m/s **40. A marksman aims a rifle to hit the bull s-eye of a target as shown in Figure 3-5. If θ = 1.5 o, and the bullet hits directly target center, how long was the bullet in flight? a. 1.4 s b. 0.7 s c. 0.1 s d. 0.07 s e. 0.01 s 32
**41. A marksman aims a rifle to hit the bull s-eye of a target as shown in Figure 3-5. If θ = 1.5 o, and the bullet hits directly target center, what was the maximum height of the bullet above the horizontal? a. 6.0 m b. 60.0 cm c. 6.0 cm d. 6.0 mm e. 0.6 mm Figure 3-6 *42. A stunt man wants to fire a rocket from a moving car so that it will land back on the car as it drives, as shown in Figure 3-6. The car moves with a constant velocity. How should the stunt man direct the rocket? a. Horizontally behind of the car b. At an angle behind the car c. Directly vertical to the car d. At an angle ahead of the car e. Horizontally ahead of the car 43. A ball rolls off horizontally from a table that is 1.25 m tall with an initial speed of 2.31 m/s. How far from the base of the table does it land? a. 9.80 m b. 4.99 m c. 2.88 m d. 2.35 m e. 1.17 m 33
44. A ball rolls off horizontally from a table that is 1.25 m tall with an initial speed of 2.31 m/s. How long does it take to strike the ground? a. 3.85 s b. 1.96 s c. 0.51 s d. 0.26 s e. 0.12 s 45. A ball rolls off horizontally from a table that is 1.2 m tall with an initial speed of 2.3 m/s. What is the magnitude of its velocity when it strikes the ground? a. 9.80 m/s b. 5.51 m/s c. 3.33 m/s d. 2.31 m/s e. 1.96 m/s 46. A litterbug drops a can from a car that is moving at 35 m/s. If the height from which it was dropped is 60 cm, how far does it travel horizontally? a. 1220 cm b. 122 cm c. 12.2 cm d. 1.2 cm e. 0.1 cm 34
Answer Key 1. d 2. c 3. a 4. e 5. b 6. a 7. c 8. c 9. e 10. e 11. c 12. d 13. c 14. e 15. d 16. d 17. c 18. a 19. c 20. b 21. d 22. b 23. e 24. d 25. b 26. d 27. d 28. a 29. d 30. a 31. a 32. d 33. c 34. c 35. d 36. b 37. c 38. e 39. a 40. b 41. b 42. c 43. e 44. c 45. b 46. a 35