Question

A stone of mass 5 Kg falls from top of a cliff 50 m high and buries 1 m in sand. Find the average resistance offered by the sand and the time it takes to penetrate.

Answer 1

K.E of ball before collision with sand=P.E at $50$m height.

Work done by resistive force=P.E at $50$m height.

$F.d=mg\times 50$

$F=\frac{5\times 10\times 50}{-1}$ negative sign due to displacement in sand is opposite to the resistance $\left(F\right)$.

$F=2500$N

Velocity before collision $w_{1}k$sand is $v=\sqrt{2g\times 50}$

$N=\sqrt{1000}=31.62$m/s

Change in momentom=$mv$

$F△t=5\times 31.62$

$t=0.0632$sesc.