Question

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 13 m/s and lands 67 meters away from the wall. How tall is the building that the child is standing on?

Answer 1

Ignoring air resistance:

Vx0 = V0 cos theta = 13m/s cos 47 degrees

= 8.9 m/s
Vy0 = V0 sin theta = 13 m/s sin 47 degrees

= 9.5 m/s

So how long does it take the ball to travel 67 meters along the x axis?

s = ut
67m = 8.9 m/s t
t = 67m/8.9 m/s = 7.53 seconds.

We now know the total flight time of the ball was 7.5 seconds.

What about it's height?

Sy - Sy0 = ut + (1/2)at^2

where Sy0 is the initial distance up the y axis (ie the height of the roof that we want to find).
Sy is the final height of the ball (i.e. ground level)
u is the initial velocity along the y axis
a is the acceleration (in this case gravity g = -9.8 m/s^2)
t is the total flight time.


slightly rearranging

-Sy0 = -sy + ut + (1/2)at^2 but sy = 0 anyway and a = -g

but sy = 0

-Sy0 = ut - (1/2) gt^2
-Sy0 = (9.5 m/s) (7.53s)- (1/2)(9.8 m/s^2) (7.53s)^2

by calculator

-Sy0 = -206. 31 meters.

Sy0 = 206 meters.