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.

A. 22.5 meters
B. 50.7 meters
C. 100 meters
D. 110 meters
E. 152.45 meters

Answer 1

Answer: Option A: 22.5 m

Explanation:

A stone is dropped from a tower. The initial velocity of the stone, u = 0.

Height of the tower, y = 100 m

Let the depth of the well be d.

Time taken of the drop of the stone, t = 5 s

The stone falls under acceleration due to gravity g = 9.81 m/s²

We will use second equation of motion:

s = u t + 0.5 g t²

⇒100 m + d = 0 + 0.5 × 9.81 m/s²× (5.00 s)²

⇒d = (122.6 - 100) m = 22.6 m ≅ 22.5 m

Thus, the correct option is A. The depth of the well is 22.5 m.