Question

A body thrown vertically up with a velocity $u$ reaches the maximum height $h$ after $T$ seconds.Which of the following statements is correct?

• A. At a height $\frac{h}{2}$ from the ground its velocity is $\frac{u}{2}$
• B. At a time T its velocity is $u$
• C. At a time 2T its velocity is $-u$
• D. At a time 2T its velocity is $\frac{u}{2}$

Answer 1

The correct option is C At a time 2T its velocity is $-u$

At height $h/2$,

$V^2-u^2=-2g\left(\frac{h}{2}\right)$
$V^2=u^2-gh$

Since, $0=u^2-2gh$

$V^2=u^2-u^2/2$

$V=u/\sqrt{2}$

$V=u-gt$

At maximum height, $V=0$
At time T, its velocity is 0
$T=\frac{u}{g}....................\left(1\right)$
at $2T,V=u-gt$
$V=u-g\left(2T\right)=u-g\times 2\left(\frac{u}{g}\right)$(from 1)
$\Rightarrow V=-u$