Question

A body of mass $m$ falls from rest through a height $h$ under gravitation acceleration $g$ and is then brought to rest by penetrating through a depth $d$ into some sand. The average deceleration of the body during penetration into sand is

• A. $\frac{gh}{d}$
• B. $\frac{gd}{h}$
• C. $\frac{g{h}^2}{d^2}$
• D. $\frac{g{h}^2}{2d^2}$

Answer 1

The correct option is A $\frac{gh}{d}$

Using equation of motion
$v^2=u^2+2as$
The body starts from rest, so $u=0$
$v^2=2gh$
Now the body starts to decelerate in the sand
$0=2gh-2ad\Rightarrow a=\frac{gh}{d}$