That's the point at which the jet stops working, but by that point you can be going quite fast. If there isn't enough air to run the jet engine, there also isn't enough air to slow you down (much).
Assuming no air resistance and 10m/s^2 gravity. I calculate that you would have to be doing ~1,100m/s (~mach 3.2 at sea level) straight up at 37km to reach 100km. Or ~1,600m/s (~mach 4.7 at sea level) at 45 degrees to perpendicular.