Question

Two persons each of mass m are standing at the two extremes of a railroad car of mass M resting on a smooth track ,the given below figure.The person on left jumps to the left with a horizontal speed u with respect to the state of the cat 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.

Answer 1

Two persons each of mass m are standing at the tow extremes of a railroad car of mass M resting on a smooth track.

Case-I:

Let the velocity of the railroad car w.r.t the earth is V when the jump of left man.

$\therefore O=-mu+(M+m)V$

$\Rightarrow V=\left(\frac{mu}{M+m}\right)$ towards right

Case-II:

When the man on the right jumps,the velocity of it w.r.t the car is u.

$\therefore O=-mu+M{V}^1$

$\Rightarrow V^1=\left(\frac{mu}{M}\right)$

(V is the change in velocity of the platform when platform itself is taken as reference assuming the car to be at rest)

$\therefore$ So,net velocity towards left (i.e. the velocity of the car w.r.t. the earth)

$=\frac{mu}{M}-\frac{mu}{(M+m)}$

$=\frac{mMu+m^{2}u-Mmu}{M(M+m)}$

$=\frac{m^{2}u}{M(M+m)}$