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Question

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, it reaches maximum height H2.
The relation between the horizontal range R of the projectile, H1 and H2 is


A

R=4H1H2

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B

R=4(H1H2)

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C

R=4(H1+H2)

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D

R=H21H22

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Solution

The correct option is A

R=4H1H2


H1=u2sin2θ2gandH2=u2sin2(90θ)2g=u2cos2θ2g
H1H2=u2sin2θ2g×u2cos2θ2g=(u2sin2θ)216g2=R216
R=4H1H2


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