Question

A student kicks a football vertically upwards, causing the football to reach a maximum height of 57.0m before falling back to the ground. Determine all unknowns and answer the following questions. Neglect drag and the initial height and horizontal motion of the football.With what speed was the football kicked? What was the footballs total flight time?

Answer 1

The final speed of the ball can be given as,

`v^2=u^2-2gh`

At the maximum height the final speed is zero.

Plug in the known values,

`\begin{gathered} (0m/s)^2=u^2-2(9.8m/s^2)(57.0\text{ m)} \\ u^2=2(9.8m/s^2)(57.0\text{ m)} \\ u=\sqrt[]{1117.2m^2s^(-2)} \\ =33.4\text{ m/s} \end{gathered}`

Therefore, the speed with which the ball was kicked is 33.4 m/s.

Also, the final speed of the ball can be expressed as,

`v=u-gt`

Plug in the known values,

`\begin{gathered} 0m/s=33.4m/s-(9.8m/s^2)t \\ t=\frac{33.4\text{ m/s}}{9.8m/s^2} \\ \approx3.41\text{ s} \end{gathered}`

The total time flight time of the ball is calculated as,

Therefore, the total flight time of the ball is 3.41 s.