Question

A bullet fired from a gun falls at a distance half of its maximum range. The angle of projection of the bullet is

• A. $45^{\circ }$
• B. $60^{\circ }$
• C. $30^{\circ }$
• D. $15^{\circ }$

Answer 1

Answer: (D)

As, we know that for a projectile motion, maximum range,
$R_{\max }=\frac{u^2}{g}$ and $h_{\max }=\frac{R_{\max }}{4}$
Given, $R=\frac{R_{\max }}{2}$
$\Rightarrow \frac{R_{\max }}{2}=\frac{u^2}{2g}=R\dots (i)$
where, $R=\frac{u^2\sin 2\theta }{g}$
Hence, $\frac{u^2\sin 2\theta }{g}=\frac{u^2}{2g}$ [From Eq. (i)]
$\Rightarrow \sin 2\theta =\frac{1}{2}$
$\Rightarrow 2\theta =30^{\circ }$
$\Rightarrow \theta =15^{\circ }$