1. The problem statement, all variables and given/known data Hot-air balloon of mass M is descending straight down with acceleration a. How much Mass must be discarded to make acceleration a the same magnitude, but directly up instead of directly down? Disregard wind resistance/lift. 2. Relevant equations The only one my book discusses in this chapter is this one: F = m * a 3. The attempt at a solution Obviously I tried plugging into the equation given, F = ma. The initial force on the balloon with its initial mass must be F = M * a. Solving for M I got M = a / F. Now is where I get lost. I need to find a certain M such that a = -a? How exactly does gravity g factor into this equation? Is the initial acceleration (a - g), while the final acceleration (-a + g)? I'm a calc II student so I understand the mathematics here, and I understand the notation of finding a general solution in terms of variables. I've just been stumped on this problem. In the grand scheme of things, this is the last problem of about a dozen for a bi-weekly homework assignment, so it shouldn't hurt my grade, but I would like to understand it better because sometimes we're randomly called to the board to show our work, and I don't want to feel like a hot air balloon.