Two bodies are projected with the same velocity. If one is projected at an angle of $30^{\circ}$ and the other

Question

Two bodies are projected with the same velocity. If one is projected at an angle of $30^{\circ}$ and the other at an angle of $60^{\circ}$ to the horizontal, the ratio of the maximum heights reached is:

Accepted Answer

1.  **Formula for Maximum Height:** The maximum height $H$ reached by a projectile is given by the equation: 
    $H = \frac{v_0^2 \sin^2 	heta}{2g}$ .
2.  **Comparison:** Since the initial velocity $v_0$ and acceleration due to gravity $g$ are the same for both bodies, the height is directly proportional to $\sin^2 	heta$.
    $H \propto \sin^2 	heta$
3.  **Calculation:**
    *   For the first body ($θ_1 = 30^{\circ}$): $H_1 \propto \sin^2 30^{\circ} = (1/2)^2 = 1/4$.
    *   For the second body ($θ_2 = 60^{\circ}$): $H_2 \propto \sin^2 60^{\circ} = (\sqrt{3}/2)^2 = 3/4$.
4.  **Ratio:**
    $\frac{H_1}{H_2} = \frac{1/4}{3/4} = \frac{1}{3}$.
    The ratio is 1 : 3.

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