Question

A ball is projected at such an angle that the horizontal range is three times the maximum height. The angle of projection of the ball is

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

Answer 1

The correct option is D ${\tan }^{-1}\left(\frac{4}{3}\right)$

Given $\frac{u^2\sin 2\theta }{g}=3\frac{u^2{\sin }^2\theta }{2g}$

$\Rightarrow \theta ={\tan }^{-1}\left(\frac{4}{3}\right)$