Question

A stone thrown upward with a speed $u$ from the top of the tower reaches the ground with a velocity $3u$. The height of the tower is

• A. $3u^2/g$
• B. $6u^2/g$
• C. $4u^2/g$
• D. $9u^2/g$

Answer 1

The correct option is C $4u^2/g$

Considering downward direction as positive,let $\text{H}$ be the height of tower.
Given $u=-u$
$v=3u$
from $3\text{rd}$ equation of motion of kinematics under gravity
$v^2-u^2=2aS$ $a=g$
here $S$ is displacement
$S=\text{H}$ as downward we have assumed positive
$\Rightarrow v^2-u^2=2gH$
$=(3u{)}^2-(-u{)}^2=2gH\Rightarrow 8u^2=2gH$
$\Rightarrow \frac{4u^2}{g}=H$