Question

A body is projected vertically up with u. Its velocity at half its maximum height is?

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

Answer 1

The correct option is D $\frac{u}{\sqrt{2}}$

For a body projected up,

$H_{max}=\frac{u^2}{2g}$

By equation

$v^2=u^2-2gh$

Putting, $h=\frac{H_{max}}{2}=\frac{u^2}{4g}$

$v^2=u^2-2g{v}^2=u^2-2g\frac{u^2}{4g}$

$=u^2-\frac{u^2}{2}$

$v^2=\frac{u^2}{2}$

$v=\frac{u}{\sqrt{2}}$