For a fixed projection speed u, the product (horizontal range) × (time of flight) is maximum when:
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For a fixed projection speed u, the product (horizontal range) × (time of flight) is maximum when:

G1 Physics · Accepted Answer

For fixed u, R = 2u²sinθcosθ/g, T = 2u sinθ/g. Therefore RT ∝ sin²θ cosθ. Maximize f = sin²θ cosθ. Using logarithmic differentiation: 2cotθ − tanθ = 0. Thus tan²θ=2, so tanθ=√2.