a baloon of mass 100kg is at 100mts from the ground . a man of 50kg mass climbs the rope of the baloon with velocity 0.3m/s relative to thebaloon. in which direction will the baloon move and with what velocity?

take downward as negative & upward as positive ....here weight of man is balanced by baloon so no net force acts in the system of baloon + man...

due to motion of man in upward direction the baloon will move in downward direction according to momentam conservation...

velocity of man = V_m wrt to baloon

let velocity of baloon is V_b then

from conservation of momentam in Y direction

m(V_m - V_b) - MV_b = 0                     ( here momentam is wrt to earth)

mV_m = (M+m)V_{b                                    ( mass of man & baloon are m & M respectively)}

V_b = mV_m/(M+m) .......

V_b = 50*0.3/150 = 0.1m/s

Approved