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Question

A projectile thrown with an initial velocity u has the same range R when the maximum height attained by it is either h1 or h2. Then R, h1 and h2 are related as


A

R=h1h2

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B

R=2h1h2

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C

R=3h1h2

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D

R=4h1h2

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Solution

The correct option is D

R=4h1h2


The range of a projectile is the same for two angles of projection θ and 90θ. For these two angles of projection, the maximum heights are
h1=v20 sin2 θ2gand h2=v20 sin2(90θ)2g=v20 cos2 θ2gh1h2=v40 sin2 θ cos2 θ4g2
Also, R=2v20sin θ cos θgR2=4v40 sin2 θ cos2θg2=16×v40 sin2 θ cos2θ4g2
R2=16 h1h2
R=4h1h2
Hence, the correct choice is (d).


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