Consider an elastic collision between a 1-kg block and a 4-kg block. The initial velocity of the 1-kg block is +5 m/s; the 4-kg block is initially at rest. What are the initial velocities of the 1-kg and the 4-kg blocks, respectively, in the center-of-mass reference frame?

The initial velocities of the 1-kg and the 4-kg blocks in the center-of-mass reference frame is 4 m/s and (-1 m/s) respectively.

Explanation:

Given that,

Mass of first block, m = 1 kg

Mass of another block, m' = 4 kg

Initial speed of 1 kg block, u = +5 m/s

Initial speed of 4 kg block, u' = 0 (it was at rest)

Let V is the velocity of the center of mass. It is given by :

So, the speed of center of mass is 1 m/s

Now, the initial velocity of 1 kg block in the center-of-mass reference frame is,  5 m/s - 1 m/s = 4 m/s

the initial velocity of 4 kg block in the center-of-mass reference frame is,  0 m/s - 1 m/s = -1 m/s

Hence, the initial velocities of the 1-kg and the 4-kg blocks in the center-of-mass reference frame is 4 m/s and (-1 m/s) respectively.

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