Question

A body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is

• A. $42{^\circ} 8'$
• B. $53^{\circ} 7'$
• C. $33^{\circ} 7'$
• D. $25^{\circ} 8'$

Answer 1

The Correct Option is B

Let a body be projected at a velocity $u$ at an angle $\theta$ with the horizontal. Then horizontal range covered is given by

$R=\frac{u^{2} \sin 2 \theta}{g}\,\,\,...$(i)
and height $H$ is
$H=\frac{u^{2} \sin ^{2} \theta}{2 g}\,\,\,...$(ii)
Given $R = 3H$
$ \therefore \frac{ u^2 \, \sin \, 2 \theta }{ g } = 3 \times \frac{ u^2 \, \sin^2 \, \theta }{ 2 g } $
Also, $ \sin 2 \theta = 2 \sin \theta \cos \theta $
$ \therefore \frac{ u^2 2 \, \sin \theta \, \cos \theta }{ g } = 3 \times \frac{ u^2 \, \sin^2 \, \theta }{ 2 g } $
$\Rightarrow 2 \cos \theta = 1.5 \sin \, \theta $
$\Rightarrow \tan \, \theta = \frac{ 2}{ 1.5 } = 1.33 $
$\Rightarrow \theta = 53^\circ \, 7' $
Hence, angle of projection is $ 53^\circ \, 7' $