Suppose an astronaut in outer space suddenly discovers that the tether connecting her to her space shuttle is cut and she is slowly drifting away from her shuttle. Assuming she is wearing a tool belt holding several wrenches, how can she move herself back towards the ship?

Throw a tool on the direction opposite to the shuttle

Step-by-step explanation:

If the astronaut throws a tool in the opposite direction of the shuttle, she exerts a force in the direction away from the shuttle, while being subject to a reaction force towards the shuttle (according to Newton's 3rd law). Since there are no drag forces in space, the acceleration acquired by the astronaut would eventually take her back to the shuttle (according to Newton's 2nd law).