Question

A stone weighing 3 kg falls from the top of a tower 100 m high and buries itself 2 m deep in the sand. The time of penetration is

• A. 0.09 sec
• B. 0.9 sec
• C. 2.1 sec
• D. 1.3 sec

Answer 1

The correct option is A 0.09 sec

The velocity of the ball before reaching the ground is given by
$v^2=u^2+2as$
$v^2=2\times 9.8\times 100$
$v=14\sqrt{10}$
Distance penetrated before coming to rest $=2m$
If the retardation experienced while penetrating is a
$v^2=u^2-2as$
$v=0$
$u^2=2as$
$a=490m/s^2$ retardation

$v=u-at$
$t=\frac{14\sqrt{10}}{490}$
$=0.09s$