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

Answer 1

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

The stone rises up till its vertical velocity is zero and again reached the top of the tower with a speed $u$(downward). The speed of the stone at the base is $3u$
WKT, $v^2=u^2+2gh$
where, $v=$ final velocity
$u=-u$ initial velocity, -ve because it is thrown upward against gravity
$a=$ acceleration due to gravity
$h=$ height or distance
$\Rightarrow {\left(3u\right)}^2={(-u)}^2+2gh$

$\Rightarrow 9u^2-u^2=2gh$

$\Rightarrow h=\frac{4u^2}{g}$