Question

A body projected up with a speed $u$ took $T$ seconds to reach the maximum height $H$. Pick out the correct statement

• 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. Same velocity at $2T$s

Answer 1

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

$v=u-gT$
$\Rightarrow T=\frac{u}{g}....\left(1\right)$

$H=uT-\frac{1}{2}g{T}^2$
In $\frac{T}{2}sec\Rightarrow h^1=u\left(\frac{T}{2}\right)-\frac{1}{2}g\frac{T^2}{4}$

Hence $h^1\ne \frac{H}{2}$
$v=u-gt$
At, $t=\frac{T}{2}$
$v=u-g\frac{T}{2}=u-\frac{u}{2}=\frac{u}{2}\left(from\right(1)T=\frac{u}{g})$
$v^2=u^2-2gH$

At $\frac{H}{2},v^2=u^2-2g\frac{H}{2}=u^2-gH\ne \frac{u^2}{4}\Rightarrow v\ne \frac{u}{2}$

Hence, option $B$ is correct.