A soccer player kicks a rock horizontally off a 41.7 m high cliff into a pool of water. If the player hears the sound of the splash 3.08 s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343 m/s.

Answer 1

Use the height of the cliff to predict the time to fall, t1.
t1 = sqrt (2H/g)= 2.917 s
The delay time to hear the splash
t2 = 3.08 - 2.917 s,
tells you how far away it hits the water, S = t2*343 = 55.9 m
which is a combination of vertical and horizontal displacement, H and X. Use the Pythagorean theorem
S^2 = H^2 + X^2
to get the horizontal displacement when the ball hits the water:
X = sqrt[(55.9)^2 - (41.7)^2] = 37.2 m

The initial speed of the rock, which was horizontal, equals X divided by the fall time, t1.