Question

Two particles are projected in air with speed $u$ at angles $\theta_1$ and $\theta_2$ (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct?
where $T_1$ and $T_2$ are the time of flight.

• A. $\theta_1 > \theta_2$
• B. $\theta_1 = \theta_2$
• C. $T_1 < T_2$
• D. $T_1 = T_2$

Answer 1

Answer: (A)

Height,
$H=\frac{u^{2}\,sin^{2}\,\theta}{2g}$
For the same speed,
$H\,\propto\,sin^{2}\theta$
$\because H_{1} > H_{2}$ (Given)
$\therefore sin^{2}\theta_{1} > sin^{2}\theta_{2}$ or
$\theta_{1} > \theta_{2}$
Time of flight,
$T=\frac{2u\,sin\,\theta}{g}$
For the same speed,
$T\,\propto\, sin\theta$
$\because \theta_{1} > \theta_{2}$ or
$sin\theta_{1} > sin\theta_{2}$
$ \Rightarrow T_{1} > T_{2}$