Two stones are projected with the same speed but making different… - Vidyadip

MCQ

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\frac{\pi^c}{3}$and its maximum height is H, then the maximum height of the other is

✓
$\frac{1}{3} H$
B
$\frac{2}{3 H }$
C
2H
D
3H

✓

Answer

Correct option: A.

$\frac{1}{3} H$

(A)
For a given speed
since horizontal ranges are same,
$\therefore \quad$ other angle is $\left(90^{\circ}-60^{\circ}\right)=30^{\circ}$
$H=\frac{u^2 \sin ^2 60^{\circ}}{2 g}=\frac{3}{4}\left(\frac{u^2}{2 g}\right)$
$H ^{\prime}=\frac{ u ^2 \sin ^2 30^{\circ}}{2 g}=\frac{1}{4}\left(\frac{ u ^2}{2 g}\right)$
$\frac{ H ^{\prime}}{ H }=\frac{1}{4} \times \frac{4}{3}$
$H^{\prime}=\frac{1}{3} H$

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