A hot air balloon (mass M) has a passenger (mass m) and is stationary in the mid air. The passenger climbs out and slides down a rope with constant velocity u relative to the balloon.
(a) Show that when the passenger is sliding down, there is no change in mechanical energy (kinetic + gravitational potential energy) of the system (Balloon + passenger). Calculate the speed of balloon.
(b) Calculate the power of the buoyancy force on the system when the man is sliding. For easy calculation, assume that volume of man is negligible compared to the balloon.
(c) If buoyancy force is doing positive work, where is this work done lost? You have proved that sum of kinetic and potential energy of the system remains constant

Answer

(a) `(m u)/(M+m)`
(b) `mg.u`