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 the work. Please help!

Solve this equation for time, t:

t = sound travel time + rock's time to fall
= H/345 + (2H/g)^1/2

Plug in H = 57.8 and the value of g (which you surely know) and crank away.

wat

To determine the time it takes for you to hear the sound of the rock hitting the bottom of the shaft, we can use the formula:

Time = distance / velocity

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

Substituting these values into the formula:

Time = 57.8 m / 345 m/s

To calculate the time, divide the distance by the velocity:

Time ≈ 0.1678 seconds

However, this time only represents the time it takes for the sound to travel from the top to the bottom of the mine shaft. To calculate the total time it takes for you to hear the sound, we need to consider the time it takes for the sound to travel back up the shaft.

The sound has to travel twice the depth of the mine shaft, which is 2 * 57.8 m = 115.6 m.

Using the formula:

Time = distance / velocity

Time = 115.6 m / 345 m/s

Time ≈ 0.3357 seconds

To get the total time, add the time it takes for the sound to travel down and the time it takes for the sound to travel back up:

Total time = 0.1678 seconds + 0.3357 seconds

Total time ≈ 0.5035 seconds

Therefore, it would take approximately 0.5035 seconds or 3.60 seconds (rounded to two decimal places) for you to hear the sound of the rock hitting the bottom of the mine shaft.