# Two particles are projected from the same point with the same speed u such that they have the same rang R, but different maximum heights $h_{1}$ and $h_{2}$. Which of the following is correct? Option 1) $R^{2}=4h_{1}h_{2}$   Option 2) $R^{2}=16h_{1}h_{2}$ Option 3) $R^{2}=2h_{1}h_{2}$ Option 4) $R^{2}=h_{1}h_{2}$

R is the same for $\theta$ and $(90-\Theta )$ angle of projection

$R=\frac{2u^{2}\sin \Theta \cos \Theta }{g}$,     $h_{1}=\frac{u^{2}\sin ^{2}\Theta }{2g}$,     $h_{2}=\frac{u^{2}\cos ^{2}\Theta }{2g}$

$R^{2}=\frac{4u^{2}\sin ^{2}\Theta }{g}$  $\frac{u^{2}\cos ^{2}\Theta }{g}$

$R^{2}=4.2h_{1}\cdot 2h_{2}=16h_{1}h_{2}$

Option 1)

$R^{2}=4h_{1}h_{2}$

Option 2)

$R^{2}=16h_{1}h_{2}$

Option 3)

$R^{2}=2h_{1}h_{2}$

Option 4)

$R^{2}=h_{1}h_{2}$

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