Final answer:
The best example of an action involving a force operating at a distance is C) A magnet attracting a metal object. This is because magnetic forces can act without direct contact between the objects involved, unlike the contact forces exemplified in the other options.
Step-by-step explanation:
Among the options given, the best example of an action that includes a force operating at a distance is C) A magnet attracting a metal object. This example represents an action at a distance because there is no physical contact between the magnet and the metal object, yet a force is exerted. Contact forces such as those in options A) A person lifting a book, B) A ball rolling down a hill, and D) Water flowing in a river involve physical interaction between the objects. In contrast, the magnetic force is an example of a long-distance force, as it can act over a gap separating the magnet and the metal object.
The principle behind this phenomenon can be explained by the concept of a field. A magnetic field emanates from the magnet, and when a ferromagnetic object like a piece of metal enters this field, a force is felt by the object. This field is what carries the force from the magnet to the metal object, and it is a characteristic of the object creating it, in this case, the magnet. Forces like gravity and magnetism are classic examples of long-distance forces where the force acts even though the two objects are not in physical contact.