Question

A body is projected up with a speed $u$ and to reach the maximum height $H$, the time taken by it, is $T$ . Which of the following statements is correct?

• A. It reaches $\frac{H}{2}$ in $\frac{T}{2}$ s
• B. It acquires velocity $\frac{u}{2}$ in $\frac{T}{2}$ s
• C. Its velocity is $\frac{u}{2}$ at $\frac{H}{2}$
• D. None of these

Answer 1

The correct option is B It acquires velocity $\frac{u}{2}$ in $\frac{T}{2}$ s

We know that for a body projected upward,
$s=ut-\frac{1}{2}g{t}^2$
For maximum height $v=0$
$\Rightarrow v=u-gt=0$
$\Rightarrow T=\frac{u}{g}$

So, $H=(s{)}_{max}=\frac{u^2}{g}-\frac{u^2}{2g}=\frac{u^2}{2g}$

$v=u-gt$
At $t=\frac{T}{2},v=u-g\left(\frac{u}{2g}\right)=\frac{u}{2}$
$v^2=u^2-2gs$
So at $s=\frac{H}{2},v^2=u^2-2g\frac{u^2}{ug}=\frac{u^2}{2}\Rightarrow v=\frac{u}{\sqrt{2}}$