Question

A ball thrown horizontally at 22.2 m/s from the roof of a building lands 36.0 m from the base of the building. how high is the building?

Answer 1

Refer to the diagram shown below.

h =  the height of the building
g = 9.8 m/s²
Wind resistance is ignored.

u = 22.2 m/s, horizontal velocity.
The initial vertical velocity is zero.

The time of flight, t, obeys the equation
h = (1/2)*g*t²
That is,
h  = 0.5*(9.8 m/s²)*(t s)² = 4.9t²
$t= \sqrt{ \frac{h}{4.9} } =0.4518 \sqrt{h}$

Because the horizontal distance traveled is 36.0 m, therefore
(22.2 m/s)*(0.4518√h) = 36.0
10.03√h = 36
√h = 3.5892
h = 12.882 m

Answer: 12.9 m  (nearest tenth)