Question

A football kicked off at an angle 20° from the ground reaches a maximum height of 4.7 m. What is the initial velocity of the kick?

Answer 1

The motion of the football that is being kicked follows a projectile path and is parabolic in shape. It has a maximum height  of meters and the angle with respect to the ground is  degrees. The maximum height is the highest position vertically that the ball could reach. From the equations of an object in a projectile motion, we use the equation (V*sin20)^2 = 2gh  in order to solve for velocity, V. We do as follows:

((V) (sin(20)))^2 = 2gh  
(V^2) (0.342^2) = 92.12 
V = √ (92.12 / 0.342^2)
V = 28.06 m/s

The initial velocity of the kick would be 28.06 m/s.