If you came upon a sign like this, you’d probably have a hard time deciding which way to go because all the arrows point in different directions. Imagine traveling several miles in one of the directions indicated by the sign. Now suppose that a friend travels the same distance in another direction indicated by the sign. You and your friend would end up in very different locations. Obviously, direction is an important component of motion.
Direction can be described in relative terms, such as up, down, in, out, left, right, forward, backward, or sideways. Direction can also be described with the cardinal directions: north, south, east, or west. On maps, cardinal directions are indicated with a compass rose. You can see one in the bottom left corner of the map in the Figure below. You can use the compass rose to find directions on the map. For example, to go to the school from Jordan’s house, you would travel from east to west. If you wanted to go on to the post office, you would change direction at the school and then travel from south to north.
Why Direction Is Important
Look again at the map above. The distance from Jordan’s house to the post office is 3 km. But if Jordan told a friend how to reach the post office from his house, he couldn’t just say “go 3 kilometers.” The friend might end up at the park instead of the post office. Jordan would have to include direction as well as distance. He could say, “go west for 2 kilometers and then go north for 1 kilometer.”
When both distance and direction are considered, motion can be represented by a vector. A vector is a measurement that has both size and direction. It may be represented by an arrow. If you are representing motion with an arrow, the length of the arrow represents distance, and the way the arrow points represents direction. The red arrows on the map above are vectors for Jordan’s route from his house to the school and from the school to the post office. If you want to learn more about vectors, watch the video at this URL:
Q: How would you draw arrows to represent the distances and directions from the post office to the park on the map in the Figure above?
A: The vectors would look like this (See Figure below):
- Direction is an important component of motion.
- A compass rose shows cardinal directions on a map.
- A vector is a measurement that has both size and direction and may be represented by an arrow. A vector can be used to represent both distance and direction of motion.
vector: Measure such as velocity that includes both size and direction; may be represented by an arrow.
At the following URL, read the introduction to vectors and try the animations. Then answer the questions below.
- Compare scalars and vectors. Give an example of each that is related to motion.
- How can the direction part of a vector be expressed as a number?
- Think of a short route you commonly take, such as the route from your home to a friend’s house or your school. Describe the direction(s) and distance(s) you travel over this route.
- What is a vector? How can an arrow represent distance and direction of motion?
- Draw vectors to represent these motions:
- moving 3 cm to the right
- moving 2 cm to the left