Question

A student drops a ball from a height of 77.0m. Determine all unknowns and answer the following questions. Neglect drag.How long did the ball remain in the air? What was the ball's speed just before striking the ground?

Answer 1

The vertical distance covered by the ball is given as,

`h=ut+(1)/(2)gt^2`

The ball is dropped from a height and it is falling freely therefore, the initial speed of the ball is zero.

Plug in the known values,

`\begin{gathered} 77.0\text{ m=(0 m/s)t+}(1)/(2)(9.8m/s^2_{})t^2 \\ t^2=\frac{2(77.0\text{ m)}}{(9.8m/s^2)} \\ t=\sqrt[]{15.71s^2} \\ =3.96\text{ s} \end{gathered}`

Therefore, the time for which ball remains in the air is 3.96 s.

The speed of the ball when it strikes on the ground is,

`v=u+gt`

Substitute the known values,

`\begin{gathered} v=0m/s+(9.8m/s^2)(3.96\text{ s)} \\ \approx38.8\text{ m/s} \end{gathered}`

Therefore, the speed of ball with which it strikes on the ground is 38.8 m/s.