Two particles are projected from ground with same initial velocities at angles $30 ° a n d 60 °$ (with horizontal). Let $R_{1} a n d R_{2}$ be their horizontal ranges, $H_{1} a n d H_{2}$ their maximum heights and $T_{1} a n d T_{2}$ are the time of flights. Then:

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$\frac{H_{1}}{R_{1}} > \frac{H_{2}}{R_{2}}$

$\frac{H_{1}}{R_{1}} < \frac{H_{2}}{R_{2}}$

$\frac{H_{1}}{T_{1}} > \frac{H_{2}}{T_{2}}$

$\frac{H_{1}}{T_{1}} < \frac{H_{2}}{T_{2}}$

answer is B, D.

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Detailed Solution

At $30 ° a n d 60 °, R_{1} = R_{2}$
Further, $H \propto \sin^{2} θ a n d T \propto \sin θ$
$∴ \frac{H}{R} \propto \sin^{2} θ$
And $\frac{H}{T} \propto \sin θ$
$\sin 60 ° > \sin 30 °$
$∴ \frac{H_{1}}{R_{1}} > \frac{H_{2}}{R_{2}} a n d \frac{H_{1}}{T_{1}} > \frac{H_{2}}{T_{2}}$