First slide

Projectile motion

Question

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 $π / 3$ and its maximum height is h₁, then the maximum height of the other will be

Moderate

A

$3 h_{1}$
B

$2 h_{1}$
C

$h_{1} / 2$
D

$h_{1} / 3$

Solution

$\begin{array}{l} \frac{h_{2}}{h_{1}} = \frac{u^{2} \sin^{2} θ_{2}}{2 g} \times \frac{2 g}{u^{2} \sin^{2} θ_{1}} \\ = \frac{\sin^{2} θ_{2}}{\sin^{2} θ_{1}} = \frac{\sin^{2} π / 6}{\sin^{2} π / 3} = \frac{1}{3} \\ \Rightarrow h_{2} = \frac{h_{1}}{3} \end{array}$

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