The Height of the Building

Calculating the Height of the Building

You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 47° from the edge of the building with an initial velocity of 21 m/s and lands 57 meters away from the wall. How tall is the building that the child is standing on?

First, split the velocity into horizontal and vertical components:

Horizontal velocity (h): 21 cos(47°) = 15.62969052 m/s

Vertical velocity (v): 21 sin(47°) = 15.35842773 m/s

Now determine how many seconds the ball had to travel to reach 57 meters:

Time (T) = 57 m / 15.62969052 m/s = 3.647 s

The height of the ball at time T is given by the equation:

d = vT - 0.5AT^2

Where:

v = initial velocity

T = time

A = acceleration due to gravity (9.8 m/s^2)

Plugging 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 * 13.30061 s^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.

What is the height of the building that the child is standing on?

The height of the building is 9.16 meters.