Question

A cricket ball is dropped from a height of 20 m. Calculate the speed of the Ball when it hits the ground and calculate the time it takes to fall through this height. ($g=10m{s}^{-2}$)

Answer 1

Here, Initial speed, u = 0

Final speed, v = ? (To be calculated)

Acceleration due to gravity, $g=10m{s}^{-2}$

And, Height, h = 20 m

Now, we know that for a freely falling body:

$v^2=u^2+2gh$

$⟹v^2={\left(0\right)}^2+2\times 10\times 20$

$⟹v^2=400$

$⟹v^2=\sqrt{400}$

$Orv=20m{s}^{-1}$

Thus, the speed of a cricket ball when it hits the ground will be 20 m/s.

Now, Initial speed, u = 0

Final speed, v = 20 m/s (Calculated above)

Acceleration due to gravity, $g=10m{s}^{-2}$

And, Time, t = ? (To be calculated)

Putting these values in the formula:

$v=u+gt$

we get

$20=0+10\times t$

$⟹t=\frac{20}{10}$

$Ort=2s$

Thus, the ball takes 2 seconds to fall through a height of 20 metres.

$Altsolution:$

$s=ut+\frac{1}{2}a{t}^2$

$s=o+\frac{1}{2}\left(10\right)t^2$

$40=10t^2$

$t=2sec$