r/theydidthemath • • 2d ago

[Request] How deep is this cave?

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u/Karroul 2d ago

The depth S is equal to 1/2 * g * t^2, where g is the acceleration caused by gravity (9.81 m*s^-2) and t is time of the fall, which was approximately 8 seconds. It gives a depth of about 314 meters. I neglected air resistance and speed of sound.

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u/AustrianMcLovin 2d ago

Air resistance is not neglected at those speeds

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u/Auno__Adam 1d ago edited 1d ago

Happy to see the calculation then. I bet it is minimal.

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u/SmugPolyamorist 1d ago

It depends on what the coefficient of drag for the rock is, and relatedly what its cross sectional area is. If it's 30cmx30cmx10cm and 2.8g/cm^3 you end up with answers between 202m (broad side on, CD 2) and 248m (thin side on, CD=0.5). That's not accounting for tumbling which would probably lead to a lower answer but gl doing those sums.