A plumber drops a coin into a well and hears the splash after 2 seconds. How deep is the well?

To determine how deep the well is based on the time it takes for the sound of the splash to reach the plumber, we need to consider both the time taken for the coin to fall and the time taken for the sound of the splash to travel back up to the top of the well.

First, let’s break down the two components:

1. Time of fall: The coin falls under the influence of gravity, which accelerates it at approximately 32 feet per second squared, assuming we are using feet as our unit of measurement (standard acceleration due to gravity). The distance (d) fallen can be calculated from the formula:

[

d = \frac{1}{2}gt^2

]

where (g) is the acceleration due to gravity and (t) is the time taken to fall.

2. Time for sound to travel: After the coin hits the water, the sound travels back up the well. The speed of sound in air is around 1,100 feet per second. The time taken for the sound to travel back up the well can be calculated using the distance of the fall and the speed of sound:

[

s = vt