Question
Find the angle of projection at which horizontal range and maximum height are equal.
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Answer
Horizontal range = Maximum height (given) $\therefore\ \frac{\text{u}^2}{\text{g}}\sin2\theta=\frac{\text{u}^2\sin^2\theta}{2\text{g}}$ $\Rightarrow\ 2\sin\theta\cos\theta=\frac{\sin^2\theta}{2}$ $[\therefore\ \sin2\theta=2\cos\theta\sin\theta]$$\tan\theta=4$
$\Rightarrow\ \theta=75^\circ58'$
$\Rightarrow\ \theta=75^\circ58'$
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