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Question

Prove that the maximum horizontal range is 4 times of the height attained by the particle.

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Solution

RangeR=u2sin2θg
and maximum height H=u2sin2θ2g
RH=u2sin2θgu2sin2θ2g=2sin2θsin2θ
or RH=2×2cosθ.sinθsin2θ=4cosθsinθ=4cosθsinθ
or R=H4cosθsinθ=4H.cotθ
For maximum range θ=450
cotθ=1
R=4H

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