posted by suzanne .
a soccer player kicks a rock horizontally off a 40.0-m-high cliff into a pool of water. if the player hears the sound of the splash 3.00 s later, what was the initial speed given to the rock? assume the speed of sound in air to be 343m/s.
Neglecting air friction, the time it will take the rock to hit the water is
sqrt(2H/g) = 2.857 seconds. That means the sound of the splash takes 3 - 2.857 = 0.143 seconds to be heard, after hitting water. Sound travelled 49.05 m in that time. Since the cliff is 40 m high, the horizontal distance travelled by the rock was (from the Pythagorean theorem)
sqrt[(49.05)^2 -(40)^2] = 28.4 m
The rock's initial speed (and constant horizontal speed) was 28.4 m/2.857 s = 9.84 m/s