Two identical projectiles are launched with the same speed at two different angles and have the same horizontal range R. Their times of flight are 5 s and 10 s. Taking g = 10 m·s⁻², what is R?
Options

Question

Two identical projectiles are launched with the same speed at two different angles and have the same horizontal range R. Their times of flight are 5 s and 10 s. Taking g = 10 m·s⁻², what is R?

G1 Physics · Accepted Answer

For the same launch speed and equal horizontal range, the two projection angles are complementary. Let the angles be θ and 90°-θ. For the projectile with time of flight 10 s: 10 = 2u sinθ ÷ g. Therefore, u sinθ = 10g ÷ 2 = 50 m·s⁻¹. For the projectile with time of flight 5 s: 5 = 2u cosθ ÷ g. Hence, u cosθ = 5g ÷ 2 = 25 m·s⁻¹. The horizontal range is R = u² sin2θ ÷ g = 2(u sinθ)(u cosθ) ÷ g. Therefore, R = 2×50×25 ÷ 10 = 250 m. Correct option: A.