A thought experiment has been bothering me. Assume an enclosed box free-falling in a constant gravity field. The box contains a person and a bowling ball at the top end. The person throws the bowling ball down (in the direction the system is falling/the direction gravity is pulling). Obviously, being a closed system, forces are all internal, so there's no net effect in that sense. But, the center of mass has shifted downward some amount more than what is due to gravity.
The question, then, is this: What does someone outside the box observe? Part of me says they don't see anything, the box appears to fall under the influence of gravity with no visible change. The other part says there's a period corresponding to the flight of the bowling ball where the box falls faster than can be accounted for by gravity.
A follow-up question that I believe is closely related is the following: Imagine jumping off a high-dive board in a cannonball position. Shortly before hitting the water, you extend your legs downward. Do you hit the water faster, slower, or with the same velocity as someone who kept their legs extended throughout the jump?