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A man of mass m clings to a rope ladder suspended below a balloon of mass M; see Fig. The balloon is stationary with respect to the ground. (a) If the man begins to climb the ladder at a speed v (with respect to the ladder), in what direction and with what speed (with respect to the Earth) will the balloon move? (b) What is the state of motion after the man stops climbing?
(a) Assume that the mass of the man is m climbing on the ladder with velocity v and the mass of the balloon is M moving downward with velocity vb .From definition of center of mass, one can writeThe negative sign in the equation highlights the fact that the balloon moves in the direction opposite to that of man, which is downwards in this case.It is important to that when the balloon moves downwards with velocity vb and the man moves upward with velocity v, the velocity with which the man appear to move relative to ground is v + vb.Therefore, the velocity with which the balloon moves downward is given as(b) When the man stops climbing up the ladder, the balloon also stops moving downwards and eventually come to rest.
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