The angle of projection for a projectile to have same horizontal range and maximum height is :

The angle of projection for a projectile to have same horizontal range and maximum height is :
  1. $\tan ^{-1}(4)$
  2. $\tan ^{-1}\left(\frac{1}{4}\right)$
  3. $\tan ^{-1}\left(\frac{1}{2}\right)$
  4. $\tan ^{-1}(2)$

Solution

$\begin{aligned} & \frac{\mathrm{u}^2 \sin 2 \theta}{\mathrm{g}}=\frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{~g}} \\ & 4 \sin \theta \cos \theta=\sin ^2 \theta \\ & 4=\tan \theta\end{aligned}$

Asked in: JEE Main 2024 (08 Apr Shift 2)

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