A ball is released from height |RECTILINEARMOTIONJEEMain2022

JEE MAIN 2022

29-07-2022 S2

Question

A ball is released from a height $h$. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$.

Select the correct option:

$t_1=(\sqrt{2}) t_2$

$t_1=(\sqrt{2}-1) t_2$

$t_2=(\sqrt{2}+1) t_1$

$t_2=(\sqrt{2}-1) t_1$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

for first $\frac{\mathrm{h}}{2}$ $$ \frac{\mathrm{h}}{2}=\frac{1}{2} \mathrm{gt}_1^2 $$ For total height h $$ \begin{aligned} & h=\frac{1}{2} g\left(t_1+t_2\right)^2 \\ & \frac{1}{\sqrt{2}}=\frac{t_1}{t_1+t_2} \\ & 1+\frac{t_2}{t_1}=\sqrt{2} \\ & \frac{t_1}{t_2}=\frac{1}{\sqrt{2}-1} \\ & t_2=(\sqrt{2}-1) t_1 \end{aligned} $$

Question Tags

JEE Main

Physics

Easy

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