Question

Two balls $A$ and $B$ are thrown with speed $u$ and $\frac{u}{2}$ respectively. Both the balls cover the same horizontal distance before returning to the horizontal plane of projection. If the angle of projection of ball $B$ is ${15}^{\circ }$ with the horizontal, then the angle of projection of $A$ is

• A. ${\sin }^{-1}\left(\frac{1}{8}\right)$
• B. $\frac{1}{2}{\sin }^{-1}\left(\frac{1}{8}\right)$
• C. $\frac{1}{3}{\sin }^{-1}\left(\frac{1}{8}\right)$
• D. $\frac{1}{4}{\sin }^{-1}\left(\frac{1}{8}\right)$

Answer 1

The correct option is B $\frac{1}{2}{\sin }^{-1}\left(\frac{1}{8}\right)$

According to question:
Range of Ball $A$= Range of Ball $B$
$\Rightarrow \frac{u^2\sin \left(2\theta \right)}{g}=\frac{{\left(\frac{u}{2}\right)}^2\sin (2\times {15}^{\circ })}{g}\Rightarrow \sin \left(2\theta \right)=\frac{1}{8}\Rightarrow \theta =\frac{1}{2}{\sin }^{-1}\left(\frac{1}{8}\right)$