A hot-air balloon consists of a basket, one passenger, and some cargo. Let the total mass be M?. Even though there is an upward lift force on the balloon, the balloon is initially accelerating downward at a rate of ?g?/3. (a) Draw a free-body diagram for the descending balloon. (b) Find the upward lift force in terms of the initial total weight ?Mg?. (c) The passenger notices that he is heading straight for a waterfall and decides he needs to go up. What fraction of the total weight must he drop overboard so that the balloon accelerates upward? at a rate of ?g?/2? Assume that the upward lift force remains the same.

Solution 56P Total mass is M. The initial acceleration of the balloon downwards was g/3. There is an upward lift by the air drag. So, the final equation for this system can be written as, Ma = Mg upward lift M × g/3 = Mg upward lift upward lift = Mg Mg/3 = Mg ---3-------------(1) a) The free body diagram is given below, b) the upward lift we found as, upward lift = Mg2 3 c) Now the balloon should go up at an acceleration of g/2....