Question

You drop a rock into a deep well. You can't see the bottom of the well but you can hear the impact after T seconds. Suppose the speed of sound is c feet per second and the depth of the falling rock at time t is gt^2/2 feet. Compute the depth d of the well. Your answer will be in terms of c, g, and T.

Answer 1

time = distance/speed, so
time for sound to return: d/c
time to fall: t = T-d/c

d/c + gt^2/2 * d/t = T

now just solve for d