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.

• A. $\theta_{1} > \theta_{2}$
• B. $\theta_{1} = \theta_{2}$
• C. $T_{1} < T_{2}$
• D. $T_{1} = T_{2}$ Where $T_{1}$and $T_{2}$are the time of flight

Answer 1

Answer: (A)

$\theta_{1} > \theta_{2}$

Answer 2

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 $\theta_{1} > \theta_{2}$ …. (i)

Time of light, $T = \frac{2u\sin\theta}{g}$

For the same speed

$T \propto \sin\theta$

$\theta_{1} > \theta_{2}$ (From (i))

$\therefore\sin\theta_{1} > \sin\theta_{2} \Rightarrow T_{1} > T_{2}$