Let's say a kid is playing basketball. He has a running start, jumps and while he is the air he shoots. There are no external forces at the time he shoots (disregard the minimal airdrag). If there are no external forces, shouldn't the center of mass after he shoots be the same as it was before he shoots? This wouldnt be true though becuase both the kid and ball move forward (because we say that he has a running start). My guess would be that the position of the center of mass doesn't necessary need to be the same, but the velocity HAS to be the same. Thus, although after the shot, both the boy and ball move forward, the velocity of the center of mass is the same as it was RIGHT before the kid shot the ball (because the kid moves forward slower but the ball forward faster). Is this correct? Another question about center of mass: Lets continue with the basketball example. This time lets say that the kid has NO running start. He jumps vertically and shoots. In this case the velocity of the mass and boy before he shoots is 0 (because he has no running start). Becuase the center of mass HAS to be the same as where it was before the kid shoots, the kid HAS to move back because the ball moves forward. This however does not happen in real life... because the kid usually comes back vertically down with no backwards displacement. Furthermore, if you watch professional NBA games, you can see that sometimes as basketball players shoot the ball when they jump, they go back very far. What causes this difference? When I shoot the ball with a jump, I come back vertically down, but when an NBA player shoots the ball, they displace backwards by a tremendous amount.