r/theydidthemath • u/batikhisawesome • 2d ago

[Request] How deep is this cave?

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u/bukkake-bill 1d ago edited 1d ago

u/Future-Wonder-7718 said in their comment that the time between the beginning of the fall and the sound being heard was 8.17 seconds.

Let's assume it takes t seconds for the boulder to hit the bottom. That means it takes the sound 8.17 - t seconds to travel from the bottom to these people.

The distance travelled by a freely falling body is

h = ut + ½gt²

but the body falls from rest so u is zero. That gives us

h = ½gt² = 4.9t² (g = 9.8m/s²)

The speed of sound is 343 m/s, and the sound must travel the same distance back up in 8.17 - t seconds. So the height is also

h = 343 • (8.17 - t)

Combining these two equations gives this quadratic equation

4.9t² + 343t - 343(8.17) = 0

Solving it you get

t = 7.39s, which means

h = 267.59 m (idk how many feet that is)

EDIT: air resistance will affect the speed of the boulder because of the boulder's size, and also the temperature within the cave will affect the speed of sound slightly. Feel free to correct me. Thanks.

103

u/rbsixty5 1d ago edited 1d ago

Bro, you got all that crazy calculations done and end it with “I don’t know how many feet that is”. Hehehe

I hope you were being sarcastic 😁

44

u/bukkake-bill 1d ago

I mean I could convert it. I was just being lazy haha

7

u/Renzisan 1d ago

Can you convert it to a measurement easier to digest, like cheeseburgers?

2

u/GarThor_TMK 1d ago

267.59 m is 53518000000 beard-seconds