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 43° from the edge of the building with an initial velocity of 17 m/s and lands 61 meters away from the wall. How tall, in meters, is the building that the child is standing on?

Answer 1

Answer:

The building is 61.19 m tall, approximately.

Explanation:

From the parabollic movement trayectory equation,

$y=H+\frac{v_{0y}}{v_x}x-\frac{1}{2v_x^2}gx^2,$

where H is the initial height of the ball and $v_{oy}$ and $v_x$ the inital velocities in the vertical and horizontal direction, respectively; we have

$H=y-\frac{v_{0y}}{v_x}x+\frac{1}{2v_x^2}gx^2$.

In this case, the ball landed at the coordinates $\left(x,y\right)=\left(61,0\right)$, so

$H=0-\frac{17\sin\left(43\deg\right)}{17\cos\left(43\deg\right)}\times 61+\frac{1}{2\left(17\cos\left(43\deg\right)\right)^2}\times 9.81\times 61^2 \approx 61.19$.