On October 14,2012, Felix Baumgartner, an Austrian sky-diver, set some new world records for his discipline. Jumping from a height of about 39 km, he reached a top speed of 1342 km/h, becoming the first human being to break the sound barrier in free fall. In order to understand some essential physics aspects of this remarkable feat, we wonder why his start height had to be that high (when the tremendous effort that was necessary for leaping from such a height required $50 million, as reported in the press). More precisely, can you give an estimate for the minimal start height--which we will call the Baumgartner limit, z[subscript B]--of a sky diver who wants to break the sound barrier in free fall?