Question

A ball is dropped off the roof of a tall building. If the ball reaches the ground in 8 seconds, how tall is the building, in meters? Round to the nearest whole number (a=9.8 m/s2)

Answer 1

Let b be the height of the building, and y the height of the ball at time t, given by

y = b - 1/2 gt²

where g = 9.8 m/s² is the magnitude of the acceleration due to gravity.

It takes the ball 8 s to reach the ground, at which point y = 0, so that

0 = b - 1/2 (9.8 m/s²) (8 s)²

b = 1/2 (9.8 m/s²) (8 s)²

b = 313.6 m