Question

The speed of a projectile at its maximum height is $\sqrt{3}/2$ times its initial speed. If the range of the projectile is $P$ times the maximum height attained by it, $P$ is equal to

• A. $\frac{4}{3}$
• B. $2\sqrt{3}$
• C. $4\sqrt{3}$
• D. $\frac{3}{4}$

Answer 1

Answer: (C)

$4\sqrt{3}$

$u\cos \theta =\left(\sqrt{3}/2\right)u$

$⟹\theta ={30}^{\circ }$

$R=\frac{u^2\sin 2\theta }{g}=\frac{\sqrt{3}{u}^2}{2g}$

$H=\frac{u^2{\sin }^2\theta }{g}=\frac{u^2}{8g}$

$\frac{R}{H}=\frac{\sqrt{3}}{2}\times 8=4\sqrt{3}$