Bob has just finished climbing a sheer cliff above a level
beach, and wants to figure out how high he climbed. All he has to
use is a baseball, a stopwatch, and a friend on the ground below
with a long measuring tape. Bob is a pitcher, and knows that the
fastest he can throw the ball is about 32.1 m/s. Bob starts the
stopwatch as he throws the ball (with no way to measure the ball's
initial trajectory), and watches carefully. The ball rises and then
falls, and after 0.910 seconds the ball is once again level with
Bob. Bob can't see well enough to time when the ball hits the
ground. Bob's friend then measures that the ball hit the ground
127 m from the base of the cliff. How high above the beach was the
ball when it was thrown?