Two projectiles are fired from the same point with the same speed and have the same horizontal range. Their times of flight are T₁ and T₂. Their common range R is:
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Two projectiles are fired from the same point with the same speed and have the same horizontal range. Their times of flight are T₁ and T₂. Their common range R is:

G1 Physics · Accepted Answer

For equal range with the same speed, the two projection angles are complementary. For the first projectile: T₁ = 2u sinθ/g. For the complementary projectile: T₂ = 2u cosθ/g. Therefore T₁T₂ = 4u²sinθcosθ/g² = 2u²sin2θ/g². But R = u²sin2θ/g. Hence R = gT₁T₂/2.