The law of motion that explains why a balloon moves in the opposite direction when air rushes out is Newton's Third Law of Motion.

Here's why:

* Newton's Third Law: For every action, there is an equal and opposite reaction.

* The Balloon: When air is forced out of the balloon, it exerts a force on the air molecules (action).

* The Reaction: The air molecules, in turn, exert an equal and opposite force on the balloon, causing it to move in the opposite direction.

In essence, the balloon is pushed forward by the escaping air. This is a classic example of how the principle of action and reaction applies in everyday situations.