How Deep Is a Mine Shaft Where It Takes Six Seconds for a Stone to Fall to the Bottom?


Quick Answer

Assuming the stone starts from rest and air resistance is negligible, the depth of the mine shaft can be found by solving the equation x = 1/2 at^2, where "x" is distance, "a" is acceleration due to gravity, and "t" is time. The answer is 176.4 meters or 588 feet.

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Full Answer

The value of a is 9.8 meters per second squared. The value of t is 6 seconds. Therefore, 0.5 x 9.8 x 36 equals 176.4 meters. In practice, air resistance extends the time it takes the stone to hit the bottom of the mine shaft by a fraction of a second. As such, the actual depth of the mine shaft would be a few meters less than the result obtained from the equation.

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