Planar Motion with Constant Acceleration

Transcription

1 Planar Motion with Constant Acceleration 1. If the acceleration vector of an object is perpendicular to its velocity vector, which of the following must be true? (a) The speed is changing. (b) The direction is changing. (c) Both the speed and the direction are changing. (d) The direction is not changing. 2. Taking up as positive at the highest point, the acceleration of a projectile is (a) always g. (b) always 0. (c) always +g. (d) +g on the way up and g on the way down. 3. A cannon ball is fired horizontally off a high cliff over a great distance. If air resistance can be ignored the path it follows is (a) part of a parabola. (b) part of a circle. (c) a hyperbola. (d) part of an ellipse. 4. Suppose that several projectiles are fired from level ground. Which one of the following will travel for longest time interval? (a) The one with the farthest range, R. (b) The one with the highest maximum elevation, h. (c) The one with the greatest initial velocity, v i. (d) The one with the smallest mass number, m. 1

2 5. Which of the following does not affect the range of a projectile? (a) v i, the magnitude of the initial velocity. (b) α, the launch angle. (c) y i, the initial height. (d) x i, the initial horizontal position. (e) All of the above affect the range of a projectile. 6. Which of the following must be zero for a projectile to achieve its maximum range? (a) ẋ f, the final x-velocity. (b) ẏ f, the final y-velocity. (c) x f, the final x-position. (d) y f, the final y-position. 7. Which of the following must be zero for a projectile to be at its maximum height? (a) ẋ, the x-velocity. (b) ẏ, the y-velocity. (c) x, the x-position. (d) y, the y-position. 8. A ball thrown from the ground happens to land on top of a roof at the instant the direction of its velocity vector is horizontal. If the magnitude of the ball s initial velocity was v i at an angle α above the horizontal, then the magnitude of the velocity when it lands on the roof is (a) zero. (b) v i sin α. (c) v i cos α. (d) v i tan α. (e) 2 v i. (f) none of the above. 2

3 9. You throw a pebble upward as shown in the figure below, with a velocity v 0 at an angle θ, from a roof (at point J) h m above the ground. If the pebble rises upward to h m above the roof (to point K), then falls to the ground below (to point L), the magnitude of its velocity when it hits the ground is (a) v 0. (b) between v 0 and 2 v 0. (c) 2 v 0. (d) greater than 2 v 0. The following sentence pertains to problems A projectile is launched from ground level with velocity v i at an angle α above the horizontal. 10. If v i were increased slightly, the range of the projectile would 11. If α were increased slightly, the time the projectile spends in the air before hitting the ground would 3

4 12. If v i were increased slightly, the maximum height attained by the projectile would 13. If α were decreased slightly, the range of the projectile would 14. A ball is thrown horizontally with a velocity v i. (a) What is its position relative to its launching point (its displacement and direction in terms of v i and g) as a function of time? (b) What is its velocity as a function of time? 15. A ball is thrown from ground-level with an initial velocity v i at an angle α above the ground. (a) What are the x- and y-components of the initial velocity? (b) What is the position (magnitude and direction) of the ball as a function of time? (c) What is the velocity (magnitude and direction) of the ball as a function of time? (d) What is the ball s highest altitude? How much time did it take to reach this position? What is the ball s velocity (magnitude and direction) at this point? (e) What is the ball s range R (assuming the ground is horizontal, what is the x-position when the ball hits the ground)? What is it s velocity (magnitude and direction) as it strikes the ground? 16. A tool slides a distance d down a smooth house roof slanted at angle α above the horizontal. The tool slides off the roof and lands on the ground a distance h below. How far (along the ground) from the house did the tool land? 4

5 17. An airplane flying horizontally at velocity v i must drop relief supplies onto a tiny, isolated island from altitude h above the surface of the island. The person in the plane charged with releasing the cargo must determine the correct instant to release it. This is done by determining the angle from vertical the target makes with the observer. What is this angle? [Hint: Draw the picture.] 5