A projectile can have the same range R for two angles of projection at a given speed. If T₁ and T₂ are the times of flight in the two cases, find their relation with R.
Options

Question

A projectile can have the same range R for two angles of projection at a given speed. If T₁ and T₂ are the times of flight in the two cases, find their relation with R.

G1 Physics · Accepted Answer

For the same range at fixed speed, the two angles are complementary: θ₂ = 90°-θ₁. Thus T₁T₂ = (2u sinθ/g)(2u cosθ/g) = 4u²sinθcosθ/g² = 2[u²sin2θ/g]/g = 2R/g. Hence option B.