A mine shaft is known to be 57.8 m deep. If you would drop a rock down the shaft, how long would it take for you to hear the sound of the rock hitting the bottom of the shaft knowing that sound travels at a constant velocity of 345 m/s?

The answer is 3.60s, but I need to work out. Please help!

To determine how long it would take for you to hear the sound of the rock hitting the bottom of the mine shaft, we need to calculate the time it takes for the sound to travel from the top to the bottom.

We can use the formula:

time = distance / velocity

In this case, the distance is the depth of the mine shaft, which is 57.8 m, and the velocity is the speed of sound, which is 345 m/s.

Plugging these values into the formula, we get:

time = 57.8 m / 345 m/s

Dividing 57.8 by 345, we find:

time = 0.1675 seconds

However, this is only the time it takes for sound to travel one way (from the top to the bottom of the shaft). To determine when you would hear the sound, we need to consider the time it takes for the sound to travel back up the shaft.

Since sound travels at a constant velocity in both directions, the time it takes for the sound to travel back is also 0.1675 seconds.

Thus, the total time it would take for you to hear the sound is the sum of the time it takes for the sound to travel down and back up the shaft:

total time = 0.1675 seconds + 0.1675 seconds = 0.335 seconds

Therefore, it would take approximately 0.335 seconds, or rounded to two decimal places, 0.34 seconds to hear the sound of the rock hitting the bottom of the mine shaft.