Dropping a Rock Down an Abandoned Coal Mine Shaft

https://www.youtube.com/shorts/qz5q20a4NJI

@tylermatthews6130
3 weeks ago
Here's some math for you

The equation for the distance traveled of a free falling object is:

h = v_0t + 1/2(gt^2)

h equals height in meters;
v_0t equals initial velocity in meters per second;
g equals acceleration due to gravity in meters per second squared;
t equals time in seconds.

The initial velocity is 0 since the rock was being held at a standstill by the man.  Simplifying the equation we get:

h = 1/2(gt^2)

I watched the video several times and came up with an approximate free fall time of 7.35 seconds.  We know that acceleration due to gravity is 9.8 m/s^2.  Plugging in the numbers we get:

h = 1/2(9.8 x 7.35^2)

Solving for h we come up with:

h = 264.71 meters

The rock fell approximately 264.71 meters, or about 868.47 feet.

Now that we have a number for distance, we can now see how much the speed of sound affects the equation.

Speed of sound is 343 meters per second

264.71 / 343 = 0.77175

The sound of the rock hitting the bottom was delayed by about 0.77 seconds, which means we need to subtract that time from the original 7.35 seconds.

7.35 - 0.77 = 6.58 seconds of free fall.

Now we have a new free fall time, and can solve for h again with the new number:

h = 1/2(gt^2)

h = 1/2(9.8 x 6.58^2)

h = 212.15

So the rock actually fell about 212.15 meters, or 696.03 feet.

Air resistance would play a role as well, so it may be more like 200 meters or 650 feet, but Ima stop there.
Show less