### Balloon with Weights

A person goes up in a balloon, with extra pieces of rock for weights..
The total mass of balloon and person and rocks is M. The balloon drops
straight down, with downward acceleration $a$. The person wants to
go up, so he starts throwing out the rocks. What is the mass of the
rocks he has to throw out, so that the balloon will have an upward
acceleration a? Assume the upward lift of the air on the balloon does
not change.