This paper investigates some of the physics behind the remarkable supersonic freefall of Felix Baumgartner accomplished with the "Red Bull Stratos" project on 14 October 2012. The underlying problem is complex: a freefall with air resistance through a medium of changing density. We developed a model for the motion within the framework of classroom physics and present a numerical approach for the dynamic solution that can be implemented by students. Our approach provides both interesting qualitative insights and accurate quantitative results for the resulting speed. (Contains 5 figures.)