Question

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

• A. ${\tan }^{-1}\left(\frac{1}{4}\right)$
• B. ${\tan }^{-1}\left(2\right)$
• C. ${\tan }^{-1}\left(4\right)$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is C ${\tan }^{-1}\left(4\right)$

We know,
$H=\frac{u^2{\sin }^2\theta }{2g}R=\frac{u^2\sin 2\theta }{g}$

As,
$H=R\frac{u^2{\sin }^2\theta }{2g}=\frac{u^2\sin 2\theta }{g}\tan \theta =4$
$\Rightarrow \theta ={\tan }^{-1}\left(4\right)$