Q85 / 90 · JEE Main 2019 (12 Apr Shift 2) · Physics

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?

A
$R^{2} = h_{1} h_{2}$
B
$R^{2} = 4 h_{1} h_{2}$
C
$R^{2} = 2 h_{1} h_{2}$
Correct answer
D
$R^{2} = 16 h_{1} h_{2}$

Solution

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}

Hence, the correct answer is option: 'D'.

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