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Q.
The body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is:
Jharkhand CECEJharkhand CECE 2003
Solution:
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
$H=\frac{u^{2} \sin ^{2} \theta}{2 g}$
Given, $R=3 H \frac{u^{2} \sin 2 \theta}{g}=3 \times \frac{u^{2} \sin ^{2} \theta}{2 g}$
or $2 \sin \theta \cos \theta=\frac{3}{2} \sin ^{2} \theta$
or $\tan \theta=\frac{4}{3}$
$\therefore \theta=\tan ^{-1}\left(\frac{4}{3}\right)=53^{\circ} 1$