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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TestHub · Accepted Answer

We get same range for angle of projections $θ$ and $90 - θ$ .
$h = \frac{u^{2} {s i n}^{2} θ}{2 g}$
$\Rightarrow h_{1} = \frac{u^{2} {s i n}^{2} θ}{2 g}, h_{2} = \frac{u^{2} {c o s}^{2} θ}{2 g}$
$h_{1} h_{2} = \frac{u^{4} {s i n}^{2} {θ c o s}^{2} θ}{4 g^{2}} = \frac{{4 u}^{4} {s i n}^{2} θ {c o s}^{2} θ}{16 g^{2}}$
$= {(\frac{u^{2} s i n 2 θ}{g})}^{2} \frac{1}{16} = \frac{R^{2}}{16}$
$∴ R^{2} = 16 h_{1} h_{2}$

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