MULTIPLE CHOICE PROBLEMS for TWO DIMENSIONAL KINEMATICS

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1 MULTIPLE CHOICE PROBLEMS for TWO DIMENSIONAL KINEMATICS MC 2D ans.doc 1 SPANGLER

2 Displacement, Velocity, and acceleration 1. A park ranger wanted to measure the height of a tall tree. The ranger stood 6.10 m from the base of the tree; and he observed that his line of sight made an angle of 73.5 above the horizontal as he looked at the top of the tree. What is the height of the tree? A) 5.84 m B) 8.77 m C) 11.7 m D) 17.3 m E) 20.6 m 2. A toolbox is carried from the base of a ladder at point A as shown. The toolbox comes to a rest on a scaffold 5 m above the ground. What is the magnitude of the displacement of the toolbox in its movement from point A to B? A) 15 m B) 19 m C) 8.1 m D) 11 m E) 13 m 3. A delivery truck leaves a warehouse and travels 2.60 km north. The truck makes a right turn and travels 1.33 km east before making another right turn and traveling 1.45 km south to arrive at its destination. What is the magnitude and direction of the truck's displacement from the warehouse? A) 1.76 km, 40.8 north of east D) 2.40 km, 45.0 north of east B) 1.15 km, 59.8 north of east E) 5.37 km, 49.2 north of east C) 1.33 km, 30.2 north of east 6. A train travels due south at 60 m/s. It reverses its direction and travels due north at 60 m/s. What is the change in velocity of the train? A) 120 m/s, due north D) 60 m/s, due south B) 120 m/s, due south E) 0 m/s C) 60 m/s, due north Projectile Motion 65. If air resistance is neglected, the motion of an object projected at an angle consists of a uniform downward acceleration combined with (a) An equal horizontal acceleration (b) A uniform horizontal velocity (c) A constant upward velocity (d) An acceleration always perpendicular to the path of motion. 12. An eagle is flying due east at 8.9 m/s carrying a gopher in its talons. The gopher manages to break free at a height of 12 m. What is the magnitude of the gopher's velocity as it reaches the ground? A) 22 m/s B) 18 m/s C) 11 m/s D) 9.8 m/s E) 8.9 m/s MC 2D ans.doc 2 SPANGLER

3 17. A football is kicked at an angle with respect to the horizontal. Which one of the following statements best describes the acceleration of the football during this event if air resistance is neglected? A) The acceleration is 0 m/s 2 at all times. B) The acceleration is 9.8 m/s 2 at all times. C) The acceleration is zero when the football has reached the highest point in its trajectory. D) The acceleration is positive as the football rises, and it is negative as the football falls. E) The acceleration starts at 9.8 m/s 2 and drops to some constant lower value as the ball approaches the ground. 18. A baseball is hit upward and travels along a parabolic arc before it strikes the ground. Which one of the following statements is necessarily true? A) The acceleration of the ball decreases as the ball moves upward. B) The velocity of the ball is zero when the ball is at the highest point in the arc. C) The acceleration of the ball is 0 m/s 2 when the ball is at the highest point in the arc. D) The x-component of the velocity of the ball is the same throughout the ball's flight. E) The velocity of the ball is a maximum when the ball is at the highest point in the arc. 19. A physics student standing on the edge of a cliff throws a stone vertically downward with an initial speed of 10 m/s. The instant before the stone hits the ground below, it is traveling at a speed of 30 m/s. If the physics student were to throw the rock horizontally outward from the cliff instead, with the same initial speed of 10 m/s, how fast would the stone be traveling just before it hits the ground? A) 10 m/s B) 20 m/s C) 30 m/s D) 40 m/s E) The height of the cliff must be specified to answer this question. 20. A tennis ball is thrown from ground level with velocity v o directed 30 above the horizontal. If it takes the ball 1.0 s to reach the top of its trajectory, what is the magnitude of the initial velocity? A) 4.9 m/s B) 9.8 m/s C) 11.3 m/s D) 19.6 m/s E) 34.4 m/s Use the following to answer questions 21-22: A projectile is fired at an angle of 60.0 above the horizontal with an initial speed of 30.0 m/s. 21. What is the magnitude of the horizontal component of the projectile's displacement at the end of 2 s? A) 30 m B) 40 m C) 10 m D) 20 m E) 50 m 22. How long does it take the projectile to reach the highest point in its trajectory? A) 1.5 s B) 2.7 s C) 4.0 s D) 6.2 s E) 9.8 s Use the following to answer questions 23-28: 23. A projectile is fired from a gun and has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. Determine the initial speed of the projectile. A) 40 m/s B) 50 m/s C) 60 m/s D) 70 m/s E) 80 m/s MC 2D ans.doc 3 SPANGLER

4 24. At what angle is the projectile fired (measured with respect to the horizontal)? A) 37 B) 40 C) 45 D) 53 E) Approximately how long does it take the projectile to reach the highest point in its trajectory? A) 1 s B) 2 s C) 4 s D) 8 s E) 16 s 26. What is the speed of the projectile when it is at the highest point in its trajectory? A) 0 m/s B) 20 m/s C) 30 m/s D) 40 m/s E) 50 m/s 27. What is the acceleration of the projectile when it reaches its maximum height? A) 0 m/s 2 B) 9.8 m/s 2, downward C) 4.9 m/s 2, downward D) Less than 9.8 m/s 2 and non-zero. E) Its magnitude is 9.8 m/s 2 and; its direction is changing. 28. What is the magnitude of the projectile's velocity just before it strikes the ground? A) 0 m/s B) 9.8 m/s C) 30 m/s D) 40 m/s E) 50 m/s 29. A spring-loaded gun is aimed horizontally and is used to launch identical balls with different initial speeds. The gun is at a fixed position above the floor. The balls are fired one at a time. If the speed of the second projectile fired is twice the speed of the first projectile fired, how is the horizontal range (denoted R in the figure) affected? A) The range for both projectiles will be the same. B) The range of the second projectile will be half as much as that of the first projectile. C) The range of the second projectile will be twice as large as that of the first projectile. D) The range of the second projectile is about 1.4 times larger than that of the first projectile. E) The range of the second projectile will be smaller than that of the first projectile by a factor of 1.4. MC 2D ans.doc 4 SPANGLER

5 30. A projectile is fired horizontally with an initial speed of 57 m/s. What are the horizontal and vertical components of its displacement 3.0 s after it is fired? Horizontal Vertical A) 44 m 29 m B) 170 m 29 m C) 170 m 44 m D) 210 m 44 m E) 210 m 0 m 31. A quarterback throws a pass at an angle of 35 above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later. Determine the distance the ball was thrown. A) 13 m B) 18 m C) 36 m D) 52 m E) 72 m Use the following to answer questions 32-34: A shell is fired with a horizontal velocity in the positive x direction from the top of an 80 m high cliff. The shell strikes the ground 1330 m from the base of the cliff. 32. Determine the initial speed of the shell. A) 4.0 m/s B) 9.8 m/s C) 82 m/s D) 170 m/s E) 330 m/s 33. What is the speed of the shell as it hits the ground? A) 4.0 m/s B) 9.8 m/s C) 82 m/s D) 170 m/s E) 330 m/s 34. What is the magnitude of the acceleration of the shell just before it strikes the ground? A) 4.0 m/s 2 B) 9.8 m/s 2 C) 82 m/s 2 D) 170 m/s 2 E) 330 m/s A cannonball is aimed 30.0 above the horizontal and is fired with an initial speed of 125 m/s at ground level. How far away from the cannon will the cannonball hit the ground? A) 125 m B) 138 m C) 695 m D) 1040 m E) 1380 m MC 2D ans.doc 5 SPANGLER

6 36. A basketball is launched with an initial speed of 8.0 m/s and follows the trajectory shown. The ball enters the basket 0.96 s after it is launched. What are the distances x and y? x y A) 5.4 m 0.73 m B) 7.7 m 0.91 m C) 5.4 m 0.91 m D) 5.7 m 0.73 m E) 5.4 m 5.4 m 37. A puck slides across a smooth, level tabletop at height H at a constant speed v o. It slides off the edge of the table and hits the floor a distance x away as shown in the figure. What is the relationship between the distances x and H? A) 2H x v 0 g B) x 2 v0 2gH C) D) E) x 2 v 0 gh 2x H v 0 g x v0 H g 38. An arrow is shot horizontally from a height of 4.9 m above the ground. The initial speed of the arrow is 45 m/s. Neglecting friction, how long will it take the arrow to hit the ground? A) 9.2 s B) 6.0 s C) 1.0 s D) 1.4 s E) 4.6 s 39. A bullet is aimed at a target on the wall a distance L away from the firing position. Because of gravity, the bullet strikes the wall a distance y below the mark as suggested in the figure. If the distance L were half as large, and the bullet had the same initial velocity, how would y be affected? E) It is not possible to determine unless numerical values are given for the distances. A) It will double. B) It will be half as large. C) It will be four times larger. D) It will be one fourth as large. MC 2D ans.doc 6 SPANGLER

7 Use the following to answer questions 40-43: A tennis ball is thrown upward at an angle from point A. It follows a parabolic trajectory and hits the ground at point D. At the instant shown, the ball is at point B. Point C represents the highest position of the ball above the ground. 40. How do the x and y components of the velocity vector of the ball compare at the points B and C? A) The velocity components are non-zero at B and zero at C. B) The x components are the same; the y component at C is 0 m/s. C) The x components are the same; the y component has a larger magnitude at C than at B. D) The x component is larger at C than at B; the y component at B points up while at C, it points downward. E) The x component is larger at B than at C; the y component at B points down while at C, it points upward. 41. How do the x and y components of the velocity vector of the ball compare at the points A and D? A) The velocity components are non-zero at A and are 0 m/s at D. B) The velocity components are the same in magnitude and direction at both points. C) The velocity components have the same magnitudes at both points, but their directions are reversed. D) The velocity components have the same magnitudes at both points, but the directions of the x components are reversed. E) The velocity components have the same magnitudes at both points, but the directions of the y components are reversed. 42. Which statement is true concerning the ball when it is at C, the highest point in its trajectory? A) The ball's velocity and acceleration are both zero. B) The ball's velocity is perpendicular to its acceleration. C) The ball's velocity is not zero, but its acceleration is zero. D) The ball's velocity is zero, but its acceleration is not zero. E) The horizontal and vertical components of the ball's velocity are equal. 43. At which point is the velocity vector changing most rapidly with time? A) A B) B C) C D) D E) It is changing at the same rate at all four points. Use the following to answer questions 44-46: A football is kicked with a speed of 18 m/s at an angle of 65 to the horizontal. 44. What are the respective horizontal and vertical components of the initial velocity of the football? A) 7.6 m/s, 16 m/s D) 13 m/s, 8.4 m/s B) 16 m/s, 7.6 m/s E) 9 m/s, 9 m/s C) 8.4 m/s, 13 m/s 45. How long is the football in the air? Neglect air resistance. A) 1.1 s B) 1.6 s C) 2.0 s D) 3.3 s E) 4.0 s MC 2D ans.doc 7 SPANGLER

8 46. How far does the football travel horizontally before it hits the ground? A) 18 m B) 25 m C) 36 m D) 48 m E) 72 m Use the following to answer questions 47-48: A rock is kicked horizontally at a speed of 10 m/s from the edge of a cliff. The rock strikes the ground 55 m from the foot of the cliff of height H as suggested in the figure. Neglect air resistance. 47. How long is the rock in the air? A) 1.0 s B) 1.2 s C) 3.4 s D) 5.5 s E) 11.2 s 48. What is the approximate value of H, the height of the cliff? A) 27 m B) 54 m C) 150 m D) 300 m E) 730 m Use the following to answer questions 49-51: A projectile is fired horizontally with an initial speed of 50.0 m/s. Neglect air resistance. 49. What is the magnitude of the displacement of the projectile 3.00 s after it is fired? A) 29.4 m B) 44.1 m C) 150 m D) 156 m E) 194 m 50. What is the speed of the projectile 3.00 s after it is fired? A) 29.4 m/s B) 50.0 m/s C) 58.0 m/s D) 79.4 m/s E) 98.6 m/s 51. What is the magnitude of the acceleration of the projectile 3.00 s after it is fired? A) 9.8 m/s 2 B) 16.6 m/s 2 C) 29.4 m/s 2 D) 5.42 m/s 2 E) 4.07 m/s 2 MC 2D ans.doc 8 SPANGLER

9 Relative Velocity Use the following to answer questions 8-11: A small boat travels 80.0 km north and then travels 60.0 km east in 1.0 hour. 8. What is the boat's displacement for the one-hour trip? A) 20 km B) 100 km C) 140 km D) 280 km E) km 9. What is the boat's average speed during the one-hour trip? A) 20 km/h B) 100 km/h C) 140 km/h D) 280 km/h E) km/h 10. What is the magnitude of the boat's average velocity for the one-hour trip? A) 20 km/h B) 100 km/h C) 140 km/h D) km/h E) km/h 11. What is the direction of the boat's average velocity for the one-hour trip? A) Due east D) 49.2 north of east B) 36.9 north of east E) 53.1 north of east C) 41.7 north of east 52. A tennis ball is thrown vertically upward in an evacuated chamber with an initial speed of 20.0 m/s at time t = 0 s. Approximately, what is the initial speed of the ball relative to an observer in a car that moves horizontally past the evacuated chamber with a constant speed of 30 m/s? A) 10 m/s B) 20 m/s C) 30 m/s D) 36 m/s E) 50 m/s 53. A motorcycle has a velocity of 15 m/s, due south as it passes a car with a velocity of 24 m/s, due north. What is the magnitude and direction of the velocity of the motorcycle as seen by the driver of the car? A) 9 m/s, north D) 39 m/s, south B) 9 m/s, south E) 39 m/s, north C) 15 m/s, north Use the following to answer questions 54-55: A football is kicked with a speed of 22 m/s at an angle of 60.0 to the positive x direction. At that instant, an observer rides past the football in a car that moves with a constant speed of 11 m/s in the positive x direction. 54. Determine the initial velocity of the ball relative to the observer in the car. A) 19 m/s in the +y direction D) 33 m/s at 60 to the +x direction B) 11 m/s in the +y direction E) 17 m/s at 60 to the +x direction C) 19 m/s at 60 to the +x direction MC 2D ans.doc 9 SPANGLER

10 55. Complete the following statement: According to the observer in the car, the ball will A) Follow a parabolic path. B) Follow a hyperbolic path. C) Follow a path that is straight up and down in the y direction. D) Follow a path that is straight across in the +x direction. E) Follow a straight line that is angled (less than 90 ) with respect to the x direction. Use the following to answer questions 56-57: Two cars approach each other on a straight and level road. Car A is traveling at 75 km/h, due north and car B is traveling at 45 km/h, due south. Both velocities are measured relative to the ground. 56. What is the velocity of car A relative to an observer in car B? A) 75 km/h, north D) 120 km/h, south B) 30 km/h, north E) 120 km/h, north C) 30 km/h, south 57. At a certain instant, the distance between the cars is 15 km. How long will it take from that instant for the two cars to meet? A) 450 s B) 900 s C) 720 s D) 1200 s E) 1900 s 58. A ferry can travel at an optimal speed of 8 km/h in still water measured relative to the shore. What is the optimal speed of the ferry, relative to the shore, if it moves perpendicular to a 6 km/h current? A) 4 km/h B) 8 km/h C) 10 km/h D) 14 km/h E) 28 km/h 59. A boat that can travel at 4.0 km/h in still water crosses a river with a current of 2.0 km/h. At what angle must the boat be pointed upstream (that is, relative to its actual path) to go straight across the river? A) 27 B) 30 C) 60 D) 63 E) 90 Use the following to answer questions 60-61: A man points his rowboat north from A to B, straight across a river of width 100 m. The river flows due east. The man starts across, rowing steadily at 0.75 m/s and reaches the other side of the river at point C, 150 m downstream from his starting point. 60. What is the speed of the river? A) 0.38 m/s B) 0.67 m/s C) 1.1 m/s D) 6.7 m/s E) 7.5 m/s MC 2D ans.doc 10 SPANGLER

11 61. While the man is crossing the river, what is his velocity relative to the shore? A) 1.35 m/s, 34 north of east D) 2.11 m/s, 34 north of east B) 2.00 m/s, 56 north of east E) 2.50 m/s, 42 north of east C) 1.74 m/s, 34 north of east 62. Two cars A and B approach each other at an intersection. Car A is traveling south at 20 m/s, while car B is traveling east at 17 m/s. What is the velocity of car A as described by the passengers in car B? A) 37 m/s, eastward D) 26 m/s, 50 south of west B) 26 m/s, 40 south of east E) 26 m/s, 40 south of west C) 26 m/s, 50 south of east 63. A passenger at rest on a flatbed train car fires a bullet straight up. The event is viewed by observers at rest on the station platform as the train moves past the platform with constant velocity. What is the trajectory of the bullet as described by the observers on the platform? A) A straight horizontal path in the direction of the train's velocity B) A straight vertical path up and down C) A circular path centered on the gun D) A straight diagonal path E) A parabolic path 64. Airplane One flies due east at 250 km/h relative to the ground. At the same time, Airplane Two flies 325 km/h, 35 north of east relative to the ground. What is the velocity of Airplane One relative to Airplane Two? A) 16 km/h, due west D) 170 km/h, 15 north of east B) 270 km/h, due north E) 190 km/h, 85 south of west C) 210 km/h, 55 south of east 66. A bicyclist is riding at a constant speed along a straight-line path. The rider throws a ball straight up to a height a few meters above her head. Ignoring air resistance, where will the ball land? A) Behind the rider B) In front of the rider C) In the same hand that threw the ball D) In the opposite hand to the one that threw it E) This cannot be determined without knowing the speed of the rider and the maximum height of the ball. 67. A basketball player is running at a constant speed of 2.5 m/s when he tosses a basketball upward with a speed of 6.0 m/s. How far does the player run before he catches the ball? Ignore air resistance. A) 3.1 m B) 4.5 m C) The ball cannot be caught because it will fall behind the player. D) 6.0 m E) 7.5 m 68. A ball is fired at an angle of 45, the angle that yields the maximum range in the absence of air resistance. What is the ratio of the ball's maximum height to its range? A) 1.0 B) 0.75 C) 0.67 D) 0.50 E) 0.25 MC 2D ans.doc 11 SPANGLER

12 Answer Key -- Chapter 3: Kinematics In Two Dimensions 1. E 2. A 3. A 4. D 5. B 6. A 7. D 8. B 9. C 10. B 11. E 12. B 13. E 14. C 15. E 16. A 17. B 18. D 19. C 20. D 21. A 22. B 23. B 24. D 25. C 26. C 27. B 28. E 29. C 30. C 31. D 32. E 33. E 34. B 35. E 36. C 37. A 38. C 39. D 40. B 41. E 42. B 43. E 44. A 45. D 46. B 47. D 48. C 49. D 50. C 51. A 52. D 53. D 54. A 55. C 56. E 57. A 58. C 59. B 60. C 61. A 62. D 63. E 64. E 65. B 66. C 67. A 68. E MC 2D ans.doc 12 SPANGLER