You drop a stone down a well. You hear the splash 2.23 s later. How deep is the well? speed of sound 343 m/s

Answer 1

Let the depth be X.
2.23 s = sound travel time + drop time

X/343 + sqrt(2X/g) = 2.23

Convert to a quadratic equation and solve for X.

(22.3 - X/343)^2 = X/4.9

Here is an iterative method instead:

Since the stone is much slower than sound, most of the 2.23 seconds will be spent with the stone falling. If it falls for 2.1 s, the well depth is 21.6 meters. The time for the sound to arrive would then be 0.063 s. The total time to hear the sound would be 2.16 s. That is not long enough. If the stone falls 2.16 s, a distance of 22.8 m, the sound returns in 0.066 s. That makes the total time about right.