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 plane of projection. If the angle of projection of ball $B$ is $15$ with the horizontal, then the angle of projection of $A$ is:

• A. $si{n}^{-1}\frac{1}{8}$
• B. $\frac{1}{2}si{n}^{-1}\frac{1}{8}$
• C. $\frac{1}{3}si{n}^{-1}\frac{1}{8}$
• D. $\frac{1}{4}si{n}^{-1}\frac{1}{8}$

Answer 1

The correct option is B $\frac{1}{2}si{n}^{-1}\frac{1}{8}$

range for both projectiles are smae

hence $R_1=R_2$

$⟹\frac{u^{2}sin2\theta }{g}=\frac{u^{2}sin2\theta }{4g}$

$\frac{u^{2}sin2\theta }{g}=\frac{u^{2}sin(2\times 15)}{4g}$

$sin2\theta =\frac{1}{8}$ $⟹\theta =\frac{1}{2}si{n}^{-1}\frac{1}{8}$