How does the ant know the way home with no guiding clues on the desert plain?
The desert ant Cataglyphis fortis lives in the plains of the Sahara desert. When one of the ants forages for food, it travels from its home nest along a haphazard search path like the one shown here. The ant may travel more than 500 m along such a complicated path over flat, featureless sand that contains no landmarks. Yet, when the ant decides to return home, it turns and then runs directly home.
The answer is in this chapter.
Physics deals with a great many quantities that have both size and direction, and it needs a special mathematical language—the language of vectors—to describe those quantities. This language is also used in engineering, the other sciences, and even in common speech. If you have ever given directions such as “Go five blocks down this street and then hang a left,” you have used the language of vectors. In fact, navigation of any sort is based on vectors, but physics and engineering also need vectors in special ways to explain phenomena involving rotation and magnetic forces, which we get to in later chapters. In this chapter, we focus on the basic language of vectors.
A particle moving along a straight line can move in only two directions. ...