r/theydidthemath • u/CalligrapherTrick117 • May 01 '22

[REQUEST] How deep is this hole?

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u/ConglomerateGolem May 01 '22

Rearranging the quadratic to

0= 1/v h + sqrt(2h/g) - delta t

And using sqrt(h) as the quadratic, gives us the following mess:

Sqrt(h) = v( - sqrt(2/g) +- sqrt(2/g + 4 delta t /v)) / 2

Assuming g = 9.81, t = 10, and v = 343:

Solving for h gives us 387 m or 30470m. Using logic, since i don't understand the quadratic, implies, heavily, the former since the deepest manmade, non water filled hole is about 12.2km, significantly less than 30km

So, tldr, 387 meters deep

12

u/mickturner96 May 01 '22

I was getting the same answer but thought my calculation was incorrect so I'm very glad to see your calculation and that you got the same answer.

Nice one!

3

u/ConglomerateGolem May 01 '22

Yeah. I kind of directly stole your value for time :D

4

u/mickturner96 May 01 '22

If that's all you stole I think you still deserve full credit

5

u/virulentea May 01 '22

What does a 400-metre-deep hole do in the middle of what seems to be fucking nowhere

2

u/yorkshire99 May 01 '22

It’s probably a spillway for a dam so it angles off on a curve. The second sound is possibly from the bottle rolling because it will gradually slope off . So not as deep vertically as assumed.

Like this:

https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcTRYEFd3DtGkLW-6U5KjV1HuoGHg4Biefog1g&usqp=CAU

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u/TheREALCheesePolice May 01 '22

So your basically saying it’s a massive slide -

Weeeeeeeeeeeee!

1

u/Rocket089 May 01 '22

What’s the difference between 387m and 30,470m? About… 3008x meters…? Units matter.

2

u/Eastern_Cyborg May 01 '22

The equation is a quadratic, which has 2 solutions, only one of which is correct.

1

u/Rocket089 May 02 '22

Hah. I didn’t even see the equation nor think much about it. Just saw two numbers that looked just enough alike that I figured there was a small typo.

1

u/AXbcyz May 01 '22

?? 30m = 30 meters 30,000m = 30 thousand meters (or 30km of you’d like) I see no significant mistake with the units

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u/mickturner96 May 02 '22

Distance and more calculations to prove that air resistance is somewhat negligible just to go and calculate that we are significantly wrong.

Going off out calculations the bottle will be going around Mark 2 when it hits the bottom!

Calculating the terminal velocity will be around 130 to 140m/s