Question

A man of mass m is on a rope ladder hanging from a free balloon of mass M. The balloon is not moving. In which direction and with what velocity will the balloon move if the man begins to climb the rope ladder with a uniform velocity v relative to the ladder?

Answer 1

Answer: The balloon will move downward with a velocity u equal to mv/(M + m).

Explanation:

Since the sum of momenta of the bodies of the system before the man moves is zero, then, when the man moves upward, the balloon should begin to go downward with such a velocity u that the sum of the momenta of the balloon and the man will again be zero. The velocity of the man relative to the earth will be w = v — u. His momentum will be mw; the momentum of the balloon will be — Mu and the sun of the momenta of the man and the balloon will be