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Question

A particle is projected with a velocity u at two different angles which are complementary to each other. If H1 and H2 are the heights attained by them in each case, find the range of the particle.

A
4H1H2
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B
2H1H2
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C
H1H2
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D
12H1H2
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Solution

The correct option is A 4H1H2
Let θ and (90θ) be the two complimentary angles of projections,
When angle of projection is θ:
Maximum height of a projectile, H1=u2sin2θ2g
Range of a projectile R=2u2sinθcosθg
When angle of projection is (90θ):
Maximum height of a projectile H2=u2sin2(90θ)2g=u2cos2θ2g
Range of a projectile R=2u2sin(90θ)cos(90θ)g
=2u2sinθcosθg
Range is same for both the angles of projection
R2=4u2sin2θcos2θg
R2=16(u2sin2θ2g)(u2cos2θ2g)
R2=16H1H2
R=4H1H2

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