Question

A body thrown vertically up with a velocity ${}^{\prime }{u}^{\prime }$ reaches a maximum height of ${}^{\prime }{h}^{\prime }$ after ${}^{\prime }{T}^{\prime }$ seconds. The correct statement among the following is:

• A. at a height $\frac{h}{2}$ from the ground its velocity is $u/2$
• B. at a time $T$ its velocity is ${}^{\prime }{u}^{\prime }$
• C. at a time ${}^{\prime }2T^{\prime }$ its velocity is $-u$
• D. at a time ${}^{\prime }2T^{\prime }$ its velocity is $-6u$

Answer 1

The correct option is C at a time ${}^{\prime }2T^{\prime }$ its velocity is $-u$

Given Initial velocity=$u$ , maximum height= $h$ ,

At maximum height, final velocity=0,

Using $v=u-gt$ $\Rightarrow 0=u-gT$ $\Rightarrow T=\frac{u}{g}$,

$\therefore 2T=2\frac{u}{g}$,

Velocity after $2T$, $v=u-g\times 2T$ $\Rightarrow v=u-g\times \frac{2u}{g}$= $-u$