Question

If you drop a ball from 30 m, how long will it take the ball to hit the ground? How fast will the same ball be going when it hits the ground?

Answer 1

In order to find the flight time, use the following formula:

`y=y_o-v_ot-(1)/(2)gt^2`

where,

y: final height = 0 m

yo: initial height = 30 m

g: gravitational acceleration constant = 9.8 m/s^2

t: time

Due to vo = 0m/s and y = 0 m, you can solve the equation above for t, as follow:

`t=\sqrt{(2y_o)/(g)}`

Then, by replacing the values of the parameters, you get:

`t=\sqrt[]{(2(30m))/((9.8m)/(s^2))}=2.47s`

Hence, the ball takes 2.74 s to hit the ground

To find the velocity just before the ball hits the ground, use the following formula:

`v=v_0+gt`

Replace the values of the parameters:

`v=(9.8m)/(s^2)\cdot2.47s=(24.2m)/(s)`

Hence, the speed of the ball is approximately 24.2 m/s