Two persons each of mass m are standing at the two extremes of a railroad car of mass M resting on a smooth track (figure 9-E10). The person on left jumps to the left with a horizontal speed u with respect to the state of the car before the jump. Thereafter, the other person jumps to the right, again with the same horizontal speed u with respect to the state of the car before his jump. Find the velocity of the car after both the persons have jumped off.
When the man on the right jumps to the left, let the recoil velocity of the railroad car be v
Applying conservation of momentum,
⇒ 0 = –mu + (m+M)v
When the man on the left jumps to the right, let the recoil velocity of the car be ‘v’
Applying conservation of momentum ⇒ 0 = mu – Mv’
Net recoil velocity of the car = v+v’
Finally, the velocity of the car after both people have jumped of
