Two projectiles are launched from the same level with the same initial speed, one at 15° and the other at 30° above the horizontal. If their horizontal ranges are in the ratio 1:x, what is x?
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Question

Two projectiles are launched from the same level with the same initial speed, one at 15° and the other at 30° above the horizontal. If their horizontal ranges are in the ratio 1:x, what is x?

G1 Physics · Accepted Answer

For a projectile launched and landing at the same level, R = u² sin(2θ) ÷ g. For θ₁ = 15°: R₁ = u² sin30° ÷ g. For θ₂ = 30°: R₂ = u² sin60° ÷ g. Therefore, R₁ ÷ R₂ = sin30° ÷ sin60° = (1 ÷ 2) ÷ (√3 ÷ 2) = 1 ÷ √3. Given R₁:R₂ = 1:x, x = √3. Correct option: B.