Question

A kicked football leaves the ground at an angle θ = 38.8° with a velocity of 22.1 m/s. a) Calculate the maximum height (m). b) the time of travel before the football hits the ground (s). c) how far away it hits the ground (m). Assume the ball leaves the foot at ground level, and ignore air resistance and rotation of the ball.

Answer 1

Given:

$\theta=38.8^\circ$

$v_0=22.1\:\rm m/s$

$g=9.81\:\rm m/s^2$

a) Calculate the maximum height (m)

$$h_{\max}=\frac{v_0^2\sin^2\theta}{2g}=\frac{22.1^2\sin^238.8^\circ}{2*9.81}=9.77\:\rm m$$

b) the time of travel before the football hits the ground 

$$t=\frac{2v_0\sin\theta}{g}=\frac{2*22.1\sin38.8^\circ}{9.81}=2.82\:\rm s$$

c) how far away it hits the ground (m)

$$L=\frac{v_0^2\sin2\theta}{g}=\frac{22.1^2\sin(2*38.8^\circ)}{9.81}=48.6\:\rm m$$