Question

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

• A. $43^{\circ }8$
• B. $25^{\circ }8$
• C. $33^{\circ }7$
• D. $53^{\circ }1$

Answer 1

Answer: (D)

Horizontal range of a body is given by
$R=\frac{u^2\sin 2\theta }{g}$
where $\theta$ is the angle at which body is projected.
The greatest height of body is given by
$H=\frac{u^2{\sin }^2\theta }{2g}$
Given, $R=3H\frac{u^2\sin 2\theta }{g}=3\times \frac{u^2{\sin }^2\theta }{2g}$
or $2\sin \theta \cos \theta =\frac{3}{2}{\sin }^2\theta$
or $\tan \theta =\frac{4}{3}$
$\therefore \theta ={\tan }^{-1}\left(\frac{4}{3}\right)=53^{\circ }1$