A stone projected with a velocity u angle θ with the horizontal reaches maximum height H1. When it is projected with velocity u at an angle π2−θ with the horizontal, it reaches maximum height H2. The relation between the horizontal range R of the projectile, H1 and H2 is

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R=4H1H2

R=4H1−H2

R=4H1+H2

R=H12H22

answer is A.

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Detailed Solution

H1=u2sin2⁡θ2g and H2=u2sin2⁡(90−θ)2g=u2cos2⁡θ2gH1H2=u2sin2⁡θ2g×u2cos2⁡θ2g=u2sin⁡2θ216g2=R216∴ R=4H1H2

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