1. The problem statement, all variables and given/known data A hot air ballon of mass M has two forces acting on it. An upward lift force and its weight due to gravity. The balloon is initially accelerating at a rate of -g/3. A)Find the upward lift force in terms of the initial weight Mg. B) What fraction of the total weight must be dropped so that he accelerates at a rate of g/2, assume that the upward lifting force remains the same as in part A. 3. The attempt at a solution F1=Ma=upward lifting force, f2=-Mg=weight A) I figured that F1/M + F2/M = -g/3 a-g=-g/3 a=2g/3 So then the upward lifting force would be F1=(2g/3)M B) This time F1/M + F2/M = g/2, but this time F2=-Mgk, k=the fraction of weight that must be dropped 2g/3 - gk = g/2, g will cancel -3k=-1/2 ==> k=1/6 However, the answer in my book gives 5/9. Where am I going wrong. Thanks!