Assume you are on a planet with a gravity constant g (instead of 32 feet per second squared) and a speed of sound c (instead of 1100 feet per second), and that you hear the impact of the rock after t seconds. Then the depth of the well is x feet, where your answer depends on g, c, and t.
To determine the depth of the well, we can use the relationship between the speed of sound and the time it takes for the sound to travel.
The time it takes for the sound to travel from the point of impact to your ears is t seconds. In this time, the sound travels at the speed of sound c.
So, the distance traveled by sound is given by:
Distance = speed × time
Distance = c × t
Now, let's consider the rock falling into the well. The rock experiences gravitational acceleration, which is given by the gravity constant g.
The distance covered by the rock as it falls during the time it takes for the sound to reach your ears is given by:
Distance = (1/2) × g × t^2
Finally, the depth of the well can be calculated by subtracting the distance traveled by sound from the distance covered by the falling rock:
Depth of the well = (1/2) × g × t^2 - c × t
Therefore, to find the depth of the well, you would need to know the values of the gravity constant g, the speed of sound c, and the time it takes for the sound to reach your ears t. Plug in these values into the equation and calculate the result.