question_answer

A person (mass m) is hanging from a rope fastened to a stationary balloon (mass M). If the person climbs along the rope, then with what velocity the balloon will move and in what direction? The velocity of the person relative to the rope is \[\upsilon \].

Answer:

                The initial momentum of the person and balloon is zero. Hence when the person climbs, the balloon will come down with such a velocity \[\upsilon \] that the total momentum be still zero. The velocity of the person dative to earth is (\[\upsilon -u\]). Hence                 \[m(\upsilon -u)-Mu=0\] or \[u=\frac{mu}{M+m}.\]