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JEE Advanced 2014Paper 1
Exam
JEE Advanced
Year
2014
Paper
Paper 1
Subject
Physics
Chapter
Motion in Two Dimensions

JEE Advanced 2014 · Paper 1 · Physics · Motion in Two Dimensions

A rocket is moving in a gravity free space with a constant...

A rocket is moving in a gravity free space with a constant acceleration of 2ms−22m{s}^{- 2} along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of 0.3ms−10.3m{s}^{- 1} relative to the rocket. At the same time, another ball is thrown in - x direction with a speed of 0.2ms−10.2m{s}^{- 1} from its right end relative to the rocket. The time in seconds when the two balls hit each other for the first time is

A rocket is moving in a gravity free space with a constant acceleration of 2m s ^ - 2 along + x direction (see figure).

Correct answer

2

Step-by-step solution

Consider motion of two balls with respect to rocket. (\frac{u^2}{2 a}=\frac{0.3 \times 0.3}{2 \times 2}=\frac{0.09}{4}=0.02 m) So, collision of two bals will take place very near to left wall.  for  BS=ut+12at2−4=−0.2t(12)2t2⇒t2+0.2t−4=0⇒ft=−0.2±0.04+162=1.9\begin{aligned} & \text{\text{ for } } B S=u t+\frac{1}{2} a t^2 \\ & -4=-0.2 t\left(\frac{1}{2}\right) 2 t^2 \Rightarrow t^2+0.2 t \\ & -4=0 \\ & \Rightarrow f t=\frac{-0.2 \pm \sqrt{0.04+16}}{2}=1.9 \end{aligned}) nearest integer (=2 \mathrm{ s})$
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