Projectile Motion
1. An object slides of off a 1.30 meter tall horizontal table and hits the floor 2.00 m from the edge of
the table. With what speed did it leave the table, and with what speed did it hit the floor?
2. A father and daughter are playing catch in their backyard. The father throws the ball at 20.0 m/s at
an angle of 30.0° above the horizontal. The daughter catches the ball without moving. How far apart
are our characters? How long is the ball in the air? What is the maximum height reached by the ball?
3. A brick is thrown from the top of a building that is 5.00 m high, at a speed of 28.0 m/s at an angle
of 20.0° above the horizontal. Where and when does it hit the ground?
4. An arrow is launched from the ground at a 45.0° angle to the horizontal. It clears the 15.0 m high
wall of a castle that is 30.0 m away from the archer. Find the initial speed of the arrow.
5. A flat, low building is 3.00 meters tall. A person starts from rest on the roof of the building, some
distance L away from its edge. At t = 0, he starts to run at a constant acceleration, runs horizontally off
of the building, and hits the ground 8.00 meters from the edge of the building at t = 5.0 seconds. Find
the person’s acceleration while on the roof of the building, and the distance L.
6. An evil person is standing at the top, and at the edge, of a 30.0 meter tall building. He throws a
bomb with a speed of 50.0 m/s at an angle of 36.9° above the horizontal (ignore the height of the evil
person). At street level, James Bond is driving on a motorcycle at 30.0 m/s, and he passes the edge of
the building at the instant the evil person throws the bomb. Bond is determined to catch the bomb at
the instant before it hits the ground, so that it doesn’t explode. Assume Bond catches the bomb at
ground level.
a) What is the maximum height above the ground reached by the bomb?
b) What is the velocity of the bomb just before Bond catches it?
c) In order to catch the bomb, should Bond speed up or slow down? With what (constant)
acceleration?
7. A certain gun can launch an explosive at a speed of 40.0 m/s at any angle above the horizontal.
This gun is on a plateau 100 m from the edge of a vertical cliff; the plateau is 50.0 m above a valley.
The explosive will only detonate if it hits the ground with a speed greater than 55.0 m/s. Note that (b)
and (c) are independent of (a).
a) For what initial launch angles will the explosive make it off the plateau and into the valley?
b) If the initial angle is 36.9°, how far from the base of the cliff will the explosive hit?; and . . .
c) Will the explosive detonate? Prove your answer! Answers without proof will receive no credit.
8. A missile is launched with an acceleration of 14.0 m/s2 up a 40.0 m long track that is inclined at
36.9° to the horizontal. Find the maximum height reached by the missile after it leaves the track, and
the point on the ground where the missile hits, as measured from the missile’s starting point on the
track.
9. A person is capable of throwing a ball with an initial speed of 25.0 m/s independent of the
throwing angle. He throws a ball at 70.0° above the horizontal; it hits the ground a certain distance D
away. T seconds after throwing the first ball, he throws a second ball at an initial angle θ above the
horizontal. The balls hit at the same place at the same time. Find D, T, and θ.
Answers:
1. V leaving table = 3.88 m/s and V hitting the floor = 6.37 m/s.
2. R = 35.3 m, t = 2.04 s, Hmax = 5.10 m
3. D = 62.7 m at t = 2.38 s
4. Initial speed = 24.2 m/s
5. a = 2.42 m/s2 and L = 21.6 m
6. a) H = 75.92 m; b) vf = 55.6 m/s @ 44° below horizontal; c) a = +2.86 m/s2 (speeding up)
7. a) 18.9° < θi < 71.1°. b) D from edge = 107 m in t = 6.47 s; c) vf = 50.8 m/s. No explosion
8. Maximum Height = 44.6 m above ground, D’ = 168 m (= 135.6 + 40 cos 36.9°)
9. D = 41.0 m ; T = 3.05 s ; θ = 20.0°.