Hey there! having a question which is from ( JEE Advanced 2014 )


A rocket is moving in a gravity free space with a constant acceleration of 2 −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 0.3 −1 relative to the rocket. At the same time, another ball is thrown in –x direction with a speed of 0.2 −1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is?
proper explanation needed~
thankyou~

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

Rocket has the acceleration in the right direction. Using this, we can say that acceleration of the right ball with respect to the left ball is 2ms−1 and the acceleration of the left ball with respect to the right ball is −2ms−1. This information is very essential in the process of finding the answer to the question.

Now, we will consider that the distance that the right ball travelled is Sm, and the distance that the left ball travelled is (4−S)m because the length of the rocket is only 4m .

To solve this question, we will need to use the equation of accelerated motion, which is:

S=ut+12at2

Where, u is the initial velocity

a is the acceleration and,

t is the time taken.

For the right ball, the equation can be written as:

S=(0.3)t+12(−2)t2

On the other hand, for the left ball, we get the equation as:

4−S=(0.2)t+12(2)t2

After substituting the value of S from one equation of the other, we can find the value of time, t, easily as:

t=8s

Hence, the correct answer is t=8s.