Q.
Trajectories of two projectiles are shown in figure. Let $T_{1}$and $T_{2}$ be the time periods and $u_{1}$ and $u_{2\ }$their speeds of projection. Then
A) $T_{2} > T_{1}$
B) $T_{1} = T_{2}$
C) $u_{1} > u_{2}$
D) $u_{1} < u_{2}$
Explanation
(d) Maximum height and time of flight depend on the vertical component of initial velocity
$H_{1} = H_{2} \Rightarrow {u_{y}}_{1} = {u_{y}}_{2}$
Here $T_{1} = T_{2}$
Range $R = \frac{u^{2}\sin{2\ \theta}}{g} = \frac{2(u\sin\theta)(u\cos\theta)}{g}$
$= \frac{2u_{x}u_{y}}{g}$
$R_{2} > R_{1}\therefore u_{x_{2}} > u_{x_{1}}\ \ or\ \ u_{2} > u_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.