Question

During a projectile motion if the maximum heigth equals 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

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

According to given condition

$H_{max}=Range$

$\frac{U^2{\sin }^2\theta }{2g}=\frac{U^2\sin 2\theta }{g}$

$\frac{{\sin }^2\theta }{2}=2\sin \theta \cos \theta$

$tan\theta =4$

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