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 s⁻²)
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Question

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 s⁻²)

G1 Physics · Accepted Answer

Projectile range is R = u² sin2θ / g For projectile A: u(A) = 40 m s⁻¹ θ(A) = 30° sin60° = √3/2 For projectile B: u(B) = 60 m s⁻¹ θ(B) = 60° sin120° = √3/2 Therefore, R(A)/R(B) = 40²/60² = 1600/3600 = 4/9 Hence the ratio is 4:9, so option C follows.