Q. Two stones are projected with the same velocity in magnitude but making different angles with the horizontal. Their ranges are equal. If the angel of projection of one is $\pi/3$ and its maximum height is $y_{1}$, the maximum height of the other will be
A) $3y_{1}$
B) $2y_{1}$
C) $\frac{y_{1}}{2}$
D) $\frac{y_{1}}{3}$
Explanation
(d) Given $\theta_{1} = \pi/3 = 30{^\circ}$
Horizontal range is same if $\theta_{1} + \theta_{2} = 90{^\circ}$
$\therefore\ \ \ \ \theta_{2} = 90{^\circ} - 30{^\circ} = 60{^\circ}$
$y_{1} = \frac{u^{2}\sin^{2}{30{^\circ}}}{2g}$ and $y_{2}\frac{u^{2}\sin^{2}{60{^\circ}}}{2g}$
$\therefore\frac{y_{2}}{y_{1}} = \frac{\sin^{2}{30{^\circ}}}{\sin^{2}{60{^\circ}}} = \left( \frac{1/4}{\sqrt{3}/4} \right)^{2}\ = \frac{1}{2}\ \ or\ \ y_{2} = \frac{y_{1}}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.