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 (π2−θ) 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=4(H1+H2)
d
R=H12H22
answer is A.
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Detailed Solution
Height reached by the stone 1st time H1=u2sin2θ2g Height reached by the stone 2nd timeH2=u2cos2θ2g H1H2=u2sinθcosθ2g But range R=u2(2sinθcosθ)g =4H1H2