I rambled about jump physics on the TIGS forum throughout the day. Here is a link.
http://forums.tigsource.com/index.php?topic=23143.msg657838#msg657838
I also wrote up some pseudocode for how to easily improve numerical integration with Velocity Verlet here.
http://forums.tigsource.com/index.php?topic=23143.msg658146#msg658146