Question

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

(1) \(\tan ^{-1}(2)\)

(2) \(\tan ^{-1}(4)\)

(3) \(\tan ^{-1}\left(\frac{1}{4}\right)\)

(4) \(\tan ^{-1}\left(\frac{1}{2}\right)\)  

Answer 1

Correct option is :  (2) \(\tan ^{-1}(4)\) 

\( \mathrm{H}_{\max }=\text { Range }\)

\(\frac{\mathrm{u}^2 \sin 2 \theta}{\mathrm{g}}=\frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{g}} \) 

\(4 \sin\theta\cos\theta=\sin^2\theta\)  

\( \mathrm{Tan} \theta=4 \) 

\(\theta=\tan ^{-1}(4)\)