Question

A body projected up with a velocity $u$ reaches a height $h$. To reach double the height, it must be projected up with a velocity of:

• A. $2u$
• B. $\frac{u}{2}$
• C. $\sqrt{2}u$
• D. $\frac{u}{\sqrt{2}}$

Answer 1

Answer: (C)

$\sqrt{2}u$

$v^2=u^2-2gh$
$v=0$ for maximum height.
So, $h\propto u^2$
So, $\frac{h_2}{h_1}=\left(\frac{u_2^2}{u_1^2}\right)$ Now $u_1=u$
If $h_2=2h_1\Rightarrow u_2=\sqrt{2}u$