# Problem: 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.

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###### Problem Details

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.