Dropping a stone down a shaft.

Classical Mechanics Level 1

I drop a stone down a vertical shaft, and I hear the stone hit the bottom after 11.4 seconds. Assuming the stone accelerates at 9.8m/s/s and the speed of sound is 350m/s, how deep is the shaft in meters?

The answer is 490.

1 solution

Caleb Townsend
Mar 14, 2015

Let $t$ be the time it takes for the stone to hit the bottom, and $s$ be the time it takes for the sound to reach you after it hits the bottom. Solve this system of equations: $4.9t^2 = 350s \\ t + s = 11.4$ The possible solutions are $t = -81.4$ and $t = 10.$ Time obviously isn't negative here so $t = 10$ and $4.9t^2 = \boxed{490\text{ m}}$

Dropping a stone down a shaft.

The answer is 490.

1 solution

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