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
Answer: 8
Solution
Both balls share the rocket's acceleration as a pseudo-acceleration of equal magnitude, so in the rocket frame their relative acceleration is zero and only their relative velocity matters. One ball moves at 0.3 m s−1 and the other at 0.2 m s−1 towards it, a closing speed of 0.5 m s−1 across the 4 m chamber, so they meet after 0.54=8 s.
JEE Advanced · 2014 · 25 May 2014 · Paper 1 · Integer answer
