A hot air balloon of mass M is stationary (with respect to the ground) in mid-air. A passenger of mass m climbs out and slides down a rope with constant
velocity v with respect to the balloon. With what velocity (magnitude and direction) relative to the ground does the balloon move? What happens if the passenger then stops sliding? Now, answer the following questions: Check, mathematically, whether energy is conserved while the passenger is sliding. Does your answer make sense? Shouldn’t there be some rubbing between the passenger’s hand and the rope? It seems that energy is “created” when both person and balloon start moving, and “lost” when both stop. How does that happen? Show, mathematically, that whatever mechanism you come up with “creates” the required energy.