Question

If the maximum height and horizontal range of a projectile are same. Then, projection angle is

• A. ${45}^{\circ }$
• B. ${30}^{\circ }$
• C. ${\tan }^{-1}3$
• D. ${\tan }^{-1}4$

Answer 1

The correct option is D ${\tan }^{-1}4$

According to question,
$R=H$
$\Rightarrow \frac{2u^2\sin \alpha \cos \alpha }{g}=\frac{u^2{\sin }^2\alpha }{2g}$
where all the symbols have their usual meaning.
$\Rightarrow \sin \alpha (2\cos \alpha -\frac{\sin \alpha }{2})=0$
$\Rightarrow \tan \alpha =4$
$\Rightarrow \alpha ={\tan }^{-1}4$.