Question

During a projectile motion, if the maximum height equals to the horizontal range, then the angle of projection with the horizontal is :-

• A. $tan^{- 1}\left(1\right)$
• B. $tan^{- 1}\left(2\right)$
• C. $tan^{- 1}\left(3\right)$
• D. $tan^{- 1}\left(4\right)$

Answer 1

Answer: (D)

$H=\frac{u^{2} s i n^{2} \theta }{2 g}$ and $R=\frac{u^{2} s i n 2 \theta }{g}$
since, $H=R$
$\frac{u^{2} s i n^{2} \theta }{2 g}=\frac{u^{2} \times 2 s i n \theta c o s \theta }{g}$
or $tan\theta =4$ or $\theta =tan^{- 1}\left(4\right)$