The time of flight of projectile is related to its horizontal ran… - Vidyadip

Question

The time of flight of projectile is related to its horizontal range as gT2 = 2R. Find the value of its angle of projection

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Answer

$\begin{aligned} g T^2 & =2 R \\ g\left(\frac{2 u \sin \theta}{g}\right)^2 & =2\left(\frac{u^2 \sin 2 \theta}{g}\right) \\ \frac{4 u^2 \sin ^2 \theta}{g} & =\frac{2 \times 2 u^2 \sin \theta \cos \theta}{g} \\ \sin \theta & =\cos \theta \\ \frac{\sin \theta}{\cos \theta} & =1=\tan 45^{\circ} \\ \tan \theta & =\tan 45^{\circ} \\ \theta & =45^{\circ}\end{aligned}$

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