Two projectiles are projected from the same point with the same speed at angles θ and (90° - θ) with the horizontal. Their horizontal ranges are equal. If the ratio of their maximum heights is 1 : 3, then tanθ is:
Options

Question

Two projectiles are projected from the same point with the same speed at angles θ and (90° - θ) with the horizontal. Their horizontal ranges are equal. If the ratio of their maximum heights is 1 : 3, then tanθ is:

Options

G1 Physics · Accepted Answer

Maximum height H ∝ sin²θ. For the complementary angle, H' ∝ cos²θ. Therefore H/H' = tan²θ = 1/3. Thus tanθ = 1/√3. Therefore option A is correct.