Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is (g = 10 m/s²) (a) 4: 9 (b) 2: √(3) (c) √(3): 2 (d) 1: 1

Answer: (a). R = (u²sin 2θ)/(g) (RA)/(RB) = (40²sin 60°)/(60²sin 120°) = (1600)/(3600) (as sin 60° = sin 120°) = 4/9, so the answer is (a) 4: 9.

Two projectiles A and B are thrown with initial velocities of 40 m/s… | JEE Main 2023 (8 Apr, Shift 1)

Q15JEE Main 2023 · 8 APR · SHIFT 1Medium

Comparing Two Projectiles

Two projectiles A and B are thrown with initial velocities of $40\text{ m/s}$ and $60\text{ m/s}$ at angles $30^\circ$ and $60^\circ$ with the horizontal respectively. The ratio of their ranges respectively is $\left(g = 10\text{ m/s}^{2}\right)$

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Answer: (a)

$R = \frac{u^2\sin 2\theta}{g}$
$\frac{R_A}{R_B} = \frac{40^2\sin 60^\circ}{60^2\sin 120^\circ} = \frac{1600}{3600}$ (as $\sin 60^\circ = \sin 120^\circ$ )
$= \frac{4}{9}$ , so the answer is (a) $4 : 9$ .

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