Question

One can get a good idea of how deep a well is, for example, by dropping a rock and listening to how long it take to hear the rock as it hits the bottom. Suppose a rock was dropped into a well that was 410 meters deep and after the rock hits the bottom, a sound wave travels at a constant speed of 303 m/s upwards until it reaches your ears and you actually hear the rock. How long will it take, in seconds, to hear the rock from the moment it is dropped?

Answer 1

Figure the time to fall:
410=1/2 g t^2 solve for time
then figure time for sound to come up:
410=vs*time
add the times.

As a practical matter, one can't hear the rock very well, it hits the sides going down, slows, bounces, so the entire process is not very accurate. I dispute that it is "good idea".