A hot- air balloon consists of a basket, one passenger, and some carge. Let the total mass be M. Even though there is an upward lift force on the balloon, the balloon is initially acceleration downwards 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.

Answer

(b) `2Mg//3; (c ) `5M//9` must be dropped;

Explanation

(a) L is the lift force.
(b) `Sigma F_(y)=ma_(y)`
`Mg-L = M(g//3)`
`L=2Mg//3` ltbr. (c ) `L-mg=m(g//2)`, where m is the mass remaining. `L=2Mg//3` so, `m=4M//9`. Mass `5M//9` must be dropped overboard.