Question

A body is thrown up with velocity $u$ to reach a height $h$. When the velocity is half the initial velocity, its height from the point of projection is:

• A. $\frac{h}{2}$
• B. $\frac{h}{4}$
• C. $\frac{3h}{4}$
• D. h

Answer 1

The correct option is C $\frac{3h}{4}$

Given initial velocity is u and maximum height is $h$.
At velocity $\frac{u}{2}$,
The displacement travelled is given by:
$\frac{u^2}{4}-u^2=2(-g)\left(h^{\prime }\right)$
$\therefore h^{\prime }=\frac{3u^2}{8g}$
But we know that, $h=\frac{u^2}{2g}$
So, $h^{\prime }=\frac{3h}{4}$