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.

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.