Q. Two projectiles $A$ and $B$ are thrown with velocities $v$ and $\frac{v}{2}$ respectively. They have the same range. If $B$ is thrown at an angle of 15${^\circ}$ to the horizontal, a must have been thrown at an angle
A) $\sin^{- 1}\left( \frac{1}{16} \right)$
B) $\sin^{- 1}\left( \frac{1}{4} \right)$
C) $2\sin^{- 1}\left( \frac{1}{4} \right)$
D) $\frac{1}{2}\sin^{- 1}\left( \frac{1}{8} \right)$
Explanation
(d) $R = \frac{v^{2}{\sin^{\ }2}\theta}{g}$
In the given problem $v^{2}\ sin2\theta =$ constant
$v^{2}\ sin2\theta = \left( \frac{v}{2} \right)^{2}\sin{30{^\circ}} = \frac{v^{2}}{8}$
or $sin2\theta = \frac{1}{8}$ or $2\theta = \sin^{- 1}\left\lbrack \frac{1}{8} \right\rbrack$ or $\theta = \frac{1}{2}\sin^{- 1}\left\lbrack \frac{1}{8} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.