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

G1 Physics · Accepted Answer

For complementary angles, T₁ = 2u sinθ/g, T₂ = 2u cosθ/g. Squaring and adding: T₁²+T₂² = 4u²(sin²θ+cos²θ)/g² = 4u²/g². Hence u = (g/2)√(T₁²+T₂²).