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, it reaches maximum height H2.
The relation between the horizontal range R of the projectile, H1 and H2 is
R=4√H1H2
H1=u2sin2θ2gandH2=u2sin2(90−θ)2g=u2cos2θ2g
H1H2=u2sin2θ2g×u2cos2θ2g=(u2sin2θ)216g2=R216
∴R=4√H1H2