A man of mass m stands on a rope ladder, which is tied to the free balloon of mass M as shown in figure. The balloon is initially at rest. The man starts to climb up the ladder with speed v relative to ladder. Find the velocity of balloon.

Let  be the velocities of the balloon and man w.r.t. ground.

Therefore velocity of man w.r.t. balloon is, 



Initially, the whole system is at rest.

Therefore the center of mass C of system is at rest.

When the man starts climbing up the ladder, he exerts force on the ladder in downward direction and he gets an equal and opposite reaction in upward direction.

Since, there is no external force on the system, therefore when the man starts climbing up, the center of mass of system remains at rest at C.


From equation (1) and (2), we have 



Negative velocity indicates that the ladder will move down.