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:

$y=y_o-v_ot-\frac{1}{2}gt^2$

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:

$t=\sqrt{\frac{2y_o}{g}}$

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

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

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:

$v=\frac{9.8m}{s^2}\cdot2.47s=\frac{24.2m}{s}$

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