a 500kg hot-air balloon takes off from rest at the surface of the earth. the nonconservative wind and lift forces take the balloon up, doing 97000 J of work on the balloon in the process. At what height above the surface of the earth does the balloon have a speed of 8.00 m/s? I stared at this question for atleast an hour and I was convinced that there is no solution. Then I tried just deducting the kinetic energy at 8.00 m/s from 97000 and using that as the gravitation protential, and I get the answer that is in the back of the book. I do not agree with this. Where does the question indicate that all of this work is done at once allowing the balloon to have 97000J of mechanical energy during the entire trip? Is not it reasonable to assume that the lift forces are constantly doing work on the balloon and therefore the balloon did not have that 97000J all along?