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Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, $h_{1}$ and $h_{2}$ which of the following is correct?

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

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

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

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

answer is D.

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Detailed Solution

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

$h_{1} h_{2} = \frac{u^{4} \sin^{2} θ \cos^{2} θ}{4 g^{2}} \times \frac{4}{4}$ $h_{1} h_{2} = \frac{R^{2}}{16}$

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