When you drop a rock into a well, you hear the splash 1.5 seconds later...

(a) How deep is the well?
(b) If the depth of the well were doubled, would the time required to hear the splash be greater than, less than, or equal to 3.0 seconds?
Explain.

The 1.5 seconds is the sum of two times.

1. time for the rock to fall, and that is
d = ½gt² or
t = √(2d/g)

2. time for the sound to return up the cliff, and that is
t = d/340
where 340 m/s is the speed of sound

so the equation is
√(2d/9.8) + d/340 = 1.5
solve for d
answer = 10.6 m
(too complicated for me to solve right now, and I long ago setup a spreadsheet to solve it for me)

if distance is doubled to 21.2 m, time is 2.14 sec

Changing the time to 3.0 s
answer is 40.7 m

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