Question

A stone is dropped from a tower 100 meters above the ground. The stone falls past ground level and into a well. It hits the water at the bottom of the well 5.00 seconds after being dropped from the tower. Calculate the depth of the well. Given: g = -9.81 meters/second2

Answer 1

Take the stone's position at ground level to be the origin, and the downward direction to be negative. Then its position in the air $y$ at time $t$ is given by

$y=100\,\mathrm m-\dfrac g2t^2$

Let $d$ be the depth of the well. The stone hits the bottom of the well after 5.00 s, so that

$-d=100\,\mathrm m-\dfrac g2(5.00\,\mathrm s)^2\implies d=\boxed{22.6\,\mathrm m}$