Two toy trains each of mass 'M' are moving in opposite directions with velocities `v_1` and `v_2` over two smooth rails. Two stuntmen of mass 'm' each are also moving with the trains (at rest w.r.t. trains). When trains are opposite to each other the stuntmen interchange their positions, then find the final velocities of the trains.

Answer

A, B

Explanation

When the stuntmen are in air (after jumping) they also have horizontal velocities `v_1` and `v_2` in opposite directions. Initially (A) and (B) were together. Similarly (C) and (D) were together.

Now, (A) will fall over (D). So this is one system and suppose velocity of this system is `V_1` (towards right or in positive direction) after jumping. Similarly, (C) will fall over (B) after jumping.
Let `V_2` is the velocity of this system towards right after jumping.
Applying conservation of linear momentum.
system 1 `p_i=p_f`
`impliesm_v_1-Mv_2=(M+m)V_1`
`implies V_1=(mv_1-Mv_2)/(M+m)`
system 2 `p_i=p_f`
`implies Mv_1-mv_2=(M+m)V_2`
`impliesV_2=(Mv_1-mv_2)/(M+m)`