1. A missile is shot horizontally from the top of a 500 m cliff with an initial speed of 300 m/s.
a) Find the time it takes for the missile to hit the ground.
b) What is the range of the missile?
c) Calculate the velocity of the missile just before it hits the ground.
d) If the missile hits the ground and bounces up at an angle of 30 degrees with a speed of 200 m/s, how far away from the point of impact will it land?
2. A good baseball pitcher can throw a fastball at about 132 ft/s (90 mph).
Assuming a constant acceleration for the ball, if he starts the ball's
motion at rest 1.5 ft behind his head and releases the ball at its final
speed 2.5 ft in front of his head (neglecting any motion of his body),
what is the acceleration of the ball during the throw?
3. A baseball is thrown from the ground into the air with an initial velocity
v = (20,10) m/s.
a) To what maximum height will the ball rise?
b) What will be the total horizontal distance traveled by the ball?
c) What is the velocity of the ball the instant before it hits the ground?
4. You get to your apartment from school after a long day and try to turn on your radio which is broken. In frustration you kick the radio out of the window which is 20 m from the ground so that the radio is moving at 30 m/s horizontally.
a) How long does it take the radio to hit the ground?
b) How far (horizontally) from window does the ball land?
c) What is the velocity of the radio just before it hits the ground?
d) How long does it take for the radio to fall halfway to the ground?
5. In the problem above, remember you kicked a radio so that it went flying out the window. Assume the radio is sitting in the window initially and it moves 0.25 m horizontally until it is traveling the 30 m/s horizontally. Answer the following questions if the radio moves under constant acceleration.
a) What is the acceleration of the radio?
b) How long did it take for the radio to reach its final velocity?
c) What is the speed of the radio after it has been accelerated for 0.1 m after it is first in contact with your foot?
6. An arrow hits a target with an initial velocity of 90 m/s. It penetrates a distance of 0.05 meters before coming to rest. Answer the following questions assuming constant acceleration.
a) Calculate the acceleration of the arrow.
b) How much time does it take for the arrow to come to rest?
c) How fast is the arrow going when it penetrates a distance of 0.015 m?
d) How far has the arrow gone into the target when the speed is 65 m/s?
7. A rock is projected straight upward with a slingshot from the ground with an initial velocity of 45 m/s. Assume no air resistance.
a) How high does the rock go?
b) How much time does it take for the rock to reach the highest point?
c) Calculate the speed of the rock when it is 20 m above the ground.
d) How far above the ground has the rock traveled when its speed is 15 m/s?8. A helicopter hovers 200 meters above the ground. The pilot throws a rock downward at 20 m/s. Answer the following questions assuming no air resistance.
a) How fast is the rock going just before it hits the ground?
b) How much time does it take to reach the ground?
c) What is the acceleration of the rock just before it hits the ground?
d) When the rock hits the ground, it makes a 0.03 meter hole before coming to rest. How much time does it take for the rock to reach this state of rest after striking the ground?
a) Calculate the acceleration of the ball while it is in contact with the player's foot.
b) How much time did it tske to accelerate the ball to the final speed.
c) Calculate the speed of the ball after the ball has been accelerated by the foot for 0.1 m.
10. A missile is fired horizontally from a fighter jet at 350 m/s relative to the ground. Answer the following questions assuming the fighter is 4500 meters above the ground.
a) How long does it take for the missile to hit the ground?
b) Find the velocity of the missile just before it hits the ground.
c) Calculate the range of the missile.
d) What is the velocity of the missile when it has fallen 500 m below the plane?
11. A cannon is fired from the top of a 25 meter tower. The cannonball is projected horizontally with an initial speed of 175 m/s.
a) How much time does it take for the cannonball to hit the ground?
b) What is the range of the cannonball?
c) What is the velocity of the cannonball just before it hits the ground?
d) How much time does it take for the cannonball to travel halfway to the ground?
12. A missile is shot from a battleship from sea level at an angle of 23o with an initial speed of 420 m/s. It flies over the level ground and lands at the same height from which it was fired.
a) Find the velocity of the missile when it first reaches 900 m above the ground?
b) How long does it take for the missile to reach its highest point?
c) How high did it go?
d) What is the range of the missile?
e) Find the velocity just before the missile hits the ground.
13. You get home after completing your physics test one Friday afternoon. Since you think you just aced the exam, you decide to open a champagne bottle in celebration. Tilting the bottle at an angle of 70o, the cork comes flying out with an initial speed of 10 m/s.
a) Find the horizontal and vertical components of the initial velocity.
b) How much time does it take for the cork to reach the highest point in its trajectory?
c) How high did it go?
d) What is the range of the cork, assuming it lands at the same height you are holding the bottle?
e) Find the velocity of the cork 0.6 seconds after the cork leaves the bottle.
14. A missile is shot at an angle of 30o from the ground with an initial speed of 300 m/s.
a) Find the horizontal and vertical components of the initial velocity.
b) How much time does it take for the missile to reach the highest point in its trajectory?
a) What is the range of the missile. Notice that this is where your target must be in order for the missile to hit it.
b) Calculate the velocity of the missile just before it hits the ground.