# How long does a ball take to fall from a roof to the ground 7 m below?

May 7, 2018

See below

#### Explanation:

If we assume that there is no air resistance and the only force acting on the ball is that of gravity, we can use the equation of motion:

$s = u t + \left(\frac{1}{2}\right) a {t}^{2}$

$s$=distance travelled
$u$=initial velocity (0)
$t$=time to travel given distance
$a$=acceleration, in this case $a = g$,the acceleration of free fall which is $9.81 m {s}^{-} 2$

Hence:
$7 = 0 t + \left(\frac{1}{2}\right) 9.81 {t}^{2}$

$7 = 0 + 4.905 {t}^{2}$

$\frac{7}{4.905} = {t}^{2}$

$t \approx 1.195 s$

So it takes barely a second for the ball to hit the ground from that height.