Question

A projectile thrown with velocity v making angle $\theta$ with vertical gains maximum height H in the time for which the projectile remains in air, the time period is

• A. $\sqrt{H\cos \theta /g}$
• B. $\sqrt{2H\cos \theta /g}$
• C. $\sqrt{4H/g}$
• D. $\sqrt{8H/g}$

Answer 1

The correct option is D $\sqrt{8H/g}$

Maximum height gained by projectile $H=\frac{v^{2}si{n}^2\varphi }{2g}$ where $\varphi ={90}^o-\theta$

$⟹$ $vsin\varphi =\sqrt{2gH}$

Time of flight $T=\frac{2vsin\varphi }{g}=\frac{2\times \sqrt{2gH}}{g}$

$⟹$ $T=\sqrt{8H/g}$