9.16 meters
First, split the velocity into horizontal and vertical components.
h = 21 cos(47°) = 21 * 0.744270977 = 15.62969052 m/s
v = 21 sin(47°) = 21 * 0.731353702 = 15.35842773 m/s
Now determine how many seconds the ball had to travel to reach 57 meters.
T = 57 m / 15.62969052 m/s = 3.647 s
height of the ball at time T is
d = vT - 0.5AT^2
where
v = initial velocity
T = Time
A = acceleration due to gravity (9.8m/s^2)
Plug in the known values
d = (15.35842773 m/s)(3.647 s) - 0.5 9.8 m/s^2 (3.647 s)^2
d = 56.01219 m - 4.9 m/s^2 (13.30061s^2)
d = 56.01219 m - 65.17298 m
d = -9.1608 m
So the ball fell a total of 9.16 meters, which means that the building was 9.16 meters tall.
