A ball is thrown up with a certain velocity so that it reaches a… | JEE Main 2021 (27 Jul, Shift 1)

Q35JEE Main 2021 · 27 JUL · SHIFT 1Medium

Motion Under Gravity

A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.

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Answer: (c)

$u^2 = 2gh$ . At height $\frac{h}{3}$ : $\frac{h}{3} = ut - \frac{1}{2}gt^2$
Roots: $t = \frac{\sqrt{2gh} \pm \sqrt{4gh/3}}{g}$
$\frac{t_1}{t_2} = \frac{\sqrt{2} - \sqrt{4/3}}{\sqrt{2} + \sqrt{4/3}}$ ; multiply top and bottom by $\sqrt{3/2}$ : $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$
So the answer is (c) $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ .

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