Practice Test: Vectors and Projectile Motion

Transcription

1 ame: Practice Test: Vectors and Projectile Motion Part A: Multiple Choice [15 points] 1. A projectile is launched at an angle of 30 0 above the horizontal. eglecting air resistance, what are the projectile s horizontal and vertical accelerations when it reaches its maximum height? [a] Both the horizontal and vertical accelerations are zero. [b] The horizontal acceleration is zero and the vertical acceleration is 9.81 m/s 2. [c] The horizontal acceleration is 9.81 m/s 2 and the vertical acceleration is zero. [d] Both the horizontal and vertical accelerations are 9.81 m/s A football player kicks a ball with an initial velocity of 25 m/s at an angle of 53 0 above the horizontal. The vertical component of the initial velocity of the ball [a] 25 m/s [b] 20. m/s [c] 15 m/s [d] 10. m/s 3. Which of the following could not be the resultant displacement of a 20 meter vector and 30 meter vector? (1) 0 m (2) 10 m (3)15 m (4) 50 m 4. A football is kicked at an angle of 25 degrees and travels 50 yards. If the football is kicked at the same speed, what other angle will allow the football to travel 50 yards? (1) 90 0 (2) 45 0 (3) 55 0 (4) A red ball and a green ball are simultaneously thrown horizontally from the same height. The red ball has an initial speed of 40. meters per second and the green ball has an initial speed of 20. meters per second. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground will be [a] the same [b] twice as much [c] half as much [d] four times as much 6. A student walks 1.0 kilometer due east and 3.0 kilometer due south. Then she runs 5.0 kilometers due west. The magnitude of the student s resultant displacement is [a] 0 km [b] 5.0 km [c] 6.0 km [4] 9.0 km 7. Two concurrent forces act on a point as shown in the diagram below. Which vector best represents their resultant? [a] [b] [c] [d]

2 8. A ball is fired with a velocity of 12 meters per second from a cannon pointing north, while the cannon is moving eastward with a velocity of 24 meters per second. Which vector best represents the resultant velocity of the ball as it leaves the cannon? [a] [c] [b] [d] 9. An archer uses a bow to fire two similar arrows with the same force. One arrow is fired at an angle of 45 0 with the horizontal and the other with an angle of 60 0 with the horizontal. Compared to the arrow fired at 60 0, the arrow fired at 45 0 has a [a] longer flight time and longer horizontal range. [b] longer flight time and shorter horizontal range. [c] shorter flight time and longer horizontal range. [d] shorter flight time and shorter horizontal range. 10. A ball is thrown at angle of 38 0 to the horizontal. What happens to the magnitude of the ball s vertical velocity during the time interval that the ball is in the air? [a] It decreases, then increases. [b] It decreases, then remains the same. [c] It increases, then decreases. [d] It remains the same. 11. A baseball is thrown at an angle of 40.0 above the horizontal. The horizontal component of the baseball s initial velocity is 12.0 meters per second. What is the magnitude of the ball s initial velocity? (a) 7.71 m/s (b) 15.7 m/s (c) 9.20 m/s (d) 18.7 m/s 12. For two vectors to give a maximum resultant, the angle between them should be (1) 0 0 (2) 45 0 (3) 90 0 (4) 180 0

3 13. The diagram represents a setup for demonstrating motion. When the lever is released, the support rod withdraws from ball B, allowing it to fall. At the same instant, the rod contacts ball A, propelling it horizontally to the left. Which statement describes the motion that is observed after the lever is released and the balls fall? [eglect friction.] (a) Ball A travels at constant velocity. (b) Ball A hits the tabletop at the same time as ball B. (c) Ball B hits the tabletop before ball A. (d) Ball B travels with an increasing acceleration. 14. A baseball player runs 27.4 meters from the batter s box to first base, overruns first base by 3.0 meters, and then returns to first base. Compared to the total distance traveled by the player, the magnitude of the player s total displacement from the batter s box is (a) 3.0 m shorter (b) 3.0 m longer (c) 6.0 m shorter (d) 6.0 m longer 15. A machine launches a tennis ball at an angle of 25 above the horizontal at a speed of 14 meters per second. The ball returns to level ground. Which combination of changes must produce an increase in time of flight of a second launch? (a) decrease the launch angle and decrease the ball s initial speed (b) decrease the launch angle and increase the ball s initial speed (c) increase the launch angle and decrease the ball s initial speed (d) increase the launch angle and increase the ball s initial speed Part II: xtended Response Questions [25 pts] 1. A person walks 150. meters due east and then walks 30. meters due west. The entire trip takes the person 10. minutes. Determine the magnitude and the direction of the person s total displacement. [2] Show work below.

4 Questions 2-6: A river has a current flowing with a velocity of 1.5 meters per second due east. A boat is leaving a dock heading 3.0 meters per second relative to the river and is headed due north as shown in the diagram. 2. The boat s velocity vector is drawn to scale as shown. Determine the scale used. 1 cm = m/s 3. Draw a correctly scaled velocity vector to show the river current on the diagram. 4. Draw a vector that illustrates the resultant velocity of the boat. 5. Calculate or find graphically the magnitude of the resultant velocity of the boat. magnitude of the boat s resultant velocity = m/s 6. Determine the angle that the boat is moving relative to east. 0

5 Questions 7-9: A ball is thrown horizontally with a speed v from a height h above ground level and strikes the ground at point X. eglect air resistance effects. v h 7. On the diagram, draw the path the ball will follow until it hits the ground. 8. Once released, what is the acceleration of the ball? X 9. If the initial speed were doubled, how would this affect the time that it would take the ball to hit the ground? Questions 10 and 11 refer to the diagram below. Key projectile A projectile B projectile C Three projectiles A, B and C are all launched from the same position at the same time and reach the same maximum height. Their trajectories are shown in the diagram above. 10. Which projectile has the greatest flight time? [a] A [b] B [c] C [d] They are all the same. 11. Which projectile was launched at the greatest speed? [a] A [b] B [c] C [d] They are all the same.

6 Questions 12-16: A football player kicks the football with a speed of 30 m/s at an angle of 50 degrees with the horizontal. All effects due to air resistance will be ignored. 30 m/s Determine the magnitude of the horizontal component of the ball's initial velocity. Show formula, substitution with units and answer with unit. [2] 13. Determine the magnitude of the vertical component of the ball's initial velocity. Show formula, substitution with units and answer with unit. [2] 14. What is the magnitude of the horizontal velocity as the ball reaches its highest point? 15. What is the magnitude of the vertical velocity when the ball reaches its highest point? 16. What is the acceleration of the football after 2.0 seconds into its flight?

7 Questions A cannon shoots a cannonball out at a 60-degree angle. The trajectory that the cannonball takes is illustrated by the curve given in the diagram below. Air resistance effects are negligible. 17. On the diagram, sketch a trajectory that the cannonball would follow if it was fired at the same speed and an angle of 30 degrees. Label this trajectory A and use a solid line to represent it. [2] 18. Compared to the flight time for the cannonball fired at 60 degrees, the flight time for the cannonball fired at 30 degrees is [a] greater [b] smaller [c] the same A soccer ball is kicked from point Pi at an angle of 45 degrees above a horizontal field. The ball follows an ideal path before landing on the field at point Pf. 19. On the diagram above, draw in the path if air resistance were taken into account. [2] 20. As compared to the horizontal component of the velocity at point Y, the horizontal component of the velocity at point X is [a] less [b] greater [c] the same