Sound Waves - Dropping a coin down a well

AI Thread Summary
When a coin is dropped into a well, and the splash sound is heard after 3.2 seconds, the calculated distance to the water surface is 46.0 meters. The quadratic equation used to solve for this distance yields two roots: 46.0 meters and an impractical 25,120 meters. The second, larger solution is not physically relevant in this context but indicates a scenario where the coin would reach the bottom significantly earlier than the sound travels back. This highlights the importance of interpreting solutions within the context of the problem. Ultimately, the valid answer for the well's depth is 46.0 meters.
Physicsman69
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The question is:

You drop a coin down a well. After 3.2 seconds you hear the sound of the coin splashing into the water surface below. How far below lies the water surface in the well?

After doing all the work the answer comes out to d = 46.0 m. However, when solving for "d" I had to solve a quadratic so I got two answers (two roots). The first was 46.0, but the other was 25,120 m. Obviously using common sense you can pick out that the correct answer was 46, but just out of curiosity what is the significance of the second answer?
 
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The other solution should be negative.

If you let a coin drop from above (using the second, negative solution), the coin arrives 3.2 seconds before a sound emitted at the same time and place (neglecting air resistance). Not what you want here, but still 3.2 seconds difference.
 
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