Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal respectively. The ratio of their respective ranges will be: (a) 1: √(2) (b) √(2): 1 (c) 2: √(3) (d) √(3): 2

Answer: (c). R ∝ sin 2θ for the same speed. (R₁)/(R₂) = (sin 90°)/(sin 60°) = (1)/(√(3)/2) = 2/√(3) So the answer is (c) 2: √(3).

Two projectiles are thrown with same initial velocity making an angle… | JEE Main 2022 (26 Jul, Shift 2)

Q16JEE Main 2022 · 26 JUL · SHIFT 2Easy

Comparing Two Projectiles

Two projectiles are thrown with same initial velocity making an angle of $45^\circ$ and $30^\circ$ with the horizontal respectively. The ratio of their respective ranges will be:

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Answer: (c)

$R \propto \sin 2\theta$ for the same speed.
$\frac{R_1}{R_2} = \frac{\sin 90^\circ}{\sin 60^\circ} = \frac{1}{\sqrt{3}/2} = \frac{2}{\sqrt{3}}$
So the answer is (c) $2 : \sqrt{3}$ .

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