What is the depth of the vertical shaft if the sound of a shot fired at the entrance to the shaft

What is the depth of the vertical shaft if the sound of a shot fired at the entrance to the shaft on the surface of the earth returned to the shooter, reflecting from the bottom of the shaft 0.5 seconds after the shot, the speed of sound in the air is considered equal to 340 m / s.

Given:

c = 340 meters per second – the speed of sound propagation in air;

t = 0.5 seconds – the time interval after which the sound from the shot returned to the shooter.

It is required to determine L (meter) – the depth of the mine.

Let the depth of the shaft be L. Then the sound from the shot reached the bottom of the shaft, and then came back, that is, passed the total distance equal to 2 * L.

The depth of the shaft will be equal to:

2 * L = c * t, from here we find:

L = c * t / 2;

L = 340 * 0.5 / 2 = 170/2 = 85 meters.

Answer: the depth of the mine is 85 meters.