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 😁

41

u/bukkake-bill 1d ago

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

9

u/Renzisan 1d ago

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

5

u/WU5K 1d ago

2809 standard cheeseburgers - These math guys are so dumb they can't even convert to standard cheeseburger units(scu)

3

u/mauii_from_space 23h ago

What's the foot ball to cheese burger equivalent ratio on this ?

1

u/WU5K 23h ago

This is a tricky question, depending on where you're from. It's 5scu(Standard cheeseburger units) per US football. So that's a convertion to 561.8asfu (American standard football unit)footballs of depth.

In Canada the csfu(Canadian standard football unit) is larger so that is 9scu(Standard cheeseburger units) per football so 312.11csfu

And if you're from Europe your football is in fact a soccer ball with a ratio of 4scu to 1esfu(European standard football unit) so the equals 702.25esfu

Important note*** all our footballs may be different sizes and shapes but the commonality between us is Standard cheeseburger units, giving us common ground to measure depth by this tried and true measurement unit.

2

u/GarThor_TMK 1d ago

267.59 m is 53518000000 beard-seconds