Question

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

• A. ${\text{tan}}^{-1}1$
• B. ${\text{tan}}^{-1}2$
• C. ${\text{tan}}^{-1}3$
• D. ${\text{tan}}^{-1}4$

Answer 1

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

We know that,
Range, $R=\frac{u^2\sin 2\theta }{g}$
Maximum height, $H_{max}=\frac{u^2{\sin }^2\theta }{2g}$
According to the question,
$R=H_{max}$
$\Rightarrow \frac{2u^2\sin \theta \cos \theta }{g}=\frac{u^2{\sin }^2\theta }{2g}$
$\Rightarrow 2\cos \theta =\frac{\sin \theta }{2}$
$\Rightarrow 4=\tan \theta$
$\to \theta ={\tan }^{-1}4$
So, option D is correct.