Question

A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d/2$. Neglecting subsequent motion and air resistance, its velocity $v$ varies with height $h$ above the ground as.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The equation $v^2-u^2=2gh$ gives velocity of the ball at a height $h$ during its downward journey as ${\overrightarrow{v}}_{down}=-\sqrt{2g(d-h)}\hat{j}$.
This velocity remains negative till the ball strikes the ground. At bouncing from the ground the ball rises to a height $d/2$.
Thus the speed just after bouncing is $u=\sqrt{gd}$. The velocity of the ball during upward motion at a height $h$ is
${\overrightarrow{v}}_{up}=-\sqrt{gd-2gh}\hat{j}$
which is positive and becomes zero at $h=d/2$.
Hence, graph (a) is correct.