Question

A rope is tied with a balloon of mass m and a man of mass m is suspending from this balloon by catching the rope in his hands. If the man starts climbing on this rope then the balloon will move with what velocity and in which direction? Velocity of man with respect to rope is v.

Answer 1

Initial momentum of man and balloon is zero, therefore on climbing upwards by man, the balloon will move downwards with velocity u such that the combined momentum of balloon and man may remains zero. The velocity of man with respect to Earth will be (v - u), therefore

m(v - u) - Mu = 0 or mv - mu = Mu

or mv = (Mu + mu)

∴ mv = u(M + m)

\(\therefore\ \mu = \frac{mv}{M + m}\)