The two projectiles are projected with the same initial velocities at the 15° and 30° with respect to the horizontal. The ratio of their ranges is 1: x. The value of x is (a) √(2) (b) √(3) (c) 2√(3) (d) 1/√(2)

Answer: (b). R ∝ sin 2θ for the same speed. (R₁)/(R₂) = (sin 30°)/(sin 60°) = (1/2)/(√(3)/2) = 1/√(3) So x = √(3), answer (b).

The two projectiles are projected with the same initial velocities at… | JEE Main 2026 (4 Apr, Shift 1)

Q2JEE Main 2026 · 4 APR · SHIFT 1Easy

Comparing Two Projectiles

The two projectiles are projected with the same initial velocities at the $15^\circ$ and $30^\circ$ with respect to the horizontal. The ratio of their ranges is $1 : x$ . The value of $x$ is

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Answer: (b)

$R \propto \sin 2\theta$ for the same speed.
$\frac{R_1}{R_2} = \frac{\sin 30^\circ}{\sin 60^\circ} = \frac{1/2}{\sqrt{3}/2} = \frac{1}{\sqrt{3}}$
So $x = \sqrt{3}$ , answer (b).

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