Question

A student is standing at the top of a 10m tall building when they kick a soccer ball off the roof at a speed of 15m/s, at an angle of 30o above the horizontal. The ball then lands on the ground, some distance from the building.

Answer 1

$g =9.8\frac{m}{s^2}$

$x_0=0; y_0=10$

$\vec v= 15\frac{m}{s}$

$\alpha=30\degree$

$\vec v= \vec v_x+\vec v_y$

$\vec v_x=\vec v\cos\alpha\approx13\frac{m}{s}$

$\vec v_y=\vec v\sin\alpha=7.5\frac{m}{s}$

$y =y_0+v_yt-\frac{gt^2}{2}$

$\text{When the ball falls to the ground:}$

$y=0$

$y_0+v_yt-\frac{gt^2}{2}=0$

$10+7.5t -4.9t^2=0$

$t =2.39s$

$x = x_0+\vec v_xt= 13*2.39=31.07 m$

$\text{Answer: distance from the building to where the ball lands is }31.07m$