Two projectiles are fired with the same speed u at complementary angles and have common range R. Their flight times, maximum heights and trajectory areas are T₁, T₂; H₁, H₂; A₁, A₂. Which relations are correct?
Select all that apply

Question

Two projectiles are fired with the same speed u at complementary angles and have common range R. Their flight times, maximum heights and trajectory areas are T₁, T₂; H₁, H₂; A₁, A₂. Which relations are correct?

Select all that apply

G1 Physics · Accepted Answer

For complementary angles θ and 90°−θ: T₁ = 2u sinθ/g, T₂ = 2u cosθ/g. Therefore T₁T₂ = 4u²sinθcosθ/g² = 2R/g. Also H₁+H₂ = u²(sin²θ+cos²θ)/(2g) = u²/(2g). For areas, A₁ = R²tanθ/6, A₂ = R²cotθ/6, so A₁A₂ = R⁴/36. Finally, T₁/T₂ = tanθ, while A₁/A₂ = tan²θ. Hence T₁/T₂ = √(A₁/A₂). All four relations are correct.

Two projectiles are fired with the same speed u at complementary angles and have common range R. Their flight times, maximum heights and trajectory areas are T₁,T₂; H₁,H₂; A₁,A₂. Which relations are correct?