Projectile Motion
1. A ball is thrown horizontally, with a speed of 15 m/s, from the top of a 6.0-meter-tall hill. How
far from the point on the ground directly below the launch point does the ball strike the
ground?
(17 m)
2. If exercise 1 were taking place on the surface of the moon, where the acceleration due to gravity
is only 1.67 m/s2, what would be the answer? (40 m)
3. One ball rolls with a constant speed of .35 m/s on a table .95 m above the floor, and another ball
rolls on the floor directly under the first ball and with the same speed and direction. Will the
balls collide after the first ball rolls off the table? If so, how far from the point directly below the
edge of the table will they be when they strike each other?
(Yes, 0.15 m)
4. A wheeled car with a spring-loaded cannon fires a metal ball vertically (look at the picture). If
the initial vertical speed of the ball is 5.0 m/s as the cannon moves horizontally with a speed of
0.75 m/s, (a) how far from the launch point does the ball fall back into the cannon? (b) What
would happen if the cannon were accelerating?
(a) 0.77 m (b) would not fall back in
5. A rifle fires a bullet with a speed of 250 m/s at an angle of 37° above the horizontal. (a) Relative
to the launch height, what height does the bullet reach? (b) How long is the bullet in the air? (c)
What is its horizontal range?
(a) 1.15 km
(b) 30.6 s
(c) 6.13 km
6. An arrow has an initial launch speed of 18 m/s. If it must strike a target 31 m away at the same
elevation, what should be the projection angle?
(35° or 55°)
7.
William Tell is shooting at an apple that hangs on a tree (picture). The apple is a horizontal
distance of 20.0 m away and at a height of 4.00 m above the ground. If the arrow is released
from a height of 1.00 m above the ground and hits the apple 0.500 s later, what is its initial
velocity?
(40.9 m/s, 11.9° above horizontal)
8. Three identical balls are thrown off a cliff at a height (h) above a horizontal plain. One ball is
projected at an angle of 45° above the horizontal, the second is thrown horizontally, and the
third is thrown at an angle of 30° below the horizontal (downward). If all of the balls have the
same initial speed, which one will have the greatest speed when it hits the ground? (Justify your
answer mathematically.)
(all have the same speed v)
9. The hole on a level, elevated golf green is a horizontal distance of 150 m from the tee and at an
elevation of 12.0 m above the tee. A golfer hits a ball at an angle 10.0° greater than that of the
hole above the tee and makes a hole-in-one! (a) What is the initial speed of the ball? (b)
Suppose the next golfer hits her ball toward the hole with the same speed but at an angle of
10.5° greater than that of the hole above the tee. Does the ball go in the hole, or is the shot too
long or too short?
(a) 66.0 m/s (b) too long