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Q.

A stone projected with a velocity u at an angle θ with the horizontal reaches maximum height H1 . When it is projected with velocity u at an angle (π2θ) with the horizontal reaches maximum height H2 . The relation between horizontal range, R of the projectile, H1 and H2 is

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a

R=4H1H2

b

R=4(H1+H2)

c

R=H12H22

d

R=4(H1H2)

answer is A.

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Detailed Solution

Height reached by the stone 1st time

H1=u2sin2θ2g

Height reached by the stone 2nd time

H2=u2cos2θ2g

H1H2=u2sinθcosθ2g

But range R=u2(2sinθcosθ)g

=4H1H2

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