Two persns each of mass m are standing at the two extremes of a railroad car of mas M resting on a smooth track figure. The person on left jumps to the left with a horizontal speed u with respect to the state f the cr before the jump. Threafter, the other person jumps to the right, again with the same horizontl speed u with respect to teg state of the car before his jump. Find the vellcity of the car after both the person hae jumped off.

Explanation

Two persons each of mass m are standing at the two extremes of a railroad car of mass M resting on smooth track.
Case I
Let the velocity of the railroad can w.r.t the earth is V when the jump of left man.
`:. O=-mu+(M+m)V`
`rarr V=((mu)/(M+m))` towards right
Case II
When the mann the right jumps the velocity of it w.r.t the car is u.
`O=mu-MV^1`
`rarr V^1=(mu)/M`
V is the change in velocity of the platform when platform itself is taken as reference assuming the car to be at rest.
`:.` So not velocity towards left (i.e. the velocity of the car w.r.t the earth)
`(mu)/M-(mu)/(M+m)`
`=(mMu+m^2u-Mmu)/(M(M+m)`
`(m^2u)/(M(M+m))`