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prove that the maximum horizontal range is 4 times the maximum height attained by a projectile which is fired long the required oblique direction

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The maximum range is achieved when θ=π/4

R = v^2 sin2θ/g
h = v^2 sin^2 θ / 2g

R/h = 4cotθ

at θ=π/4, R/h = 4

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