A person of mass m is hanging from a rope fastened to a stationary balloon of mass M If the person climbs the rope , then with what velocity the balloon would move and in what direction ?

Explanation

Let upsilon be the velocity of person climbing up the rope . As initial momentum of the person and balloon is zero , the ballon will moves down with such a velocity u that total momentum continues to bre zero . As relative velocity of person relative to earth is (upsilon - u ) , therefore
` m (upsilon - u ) - "Mu" = 0 or m upsilon = (M + m ) u `
`or u = (m upsilon)/(M+ m ) ` .