# CIESE -Navigational Vectors - Lesson #2

Lesson #1 |
Graphical Addition of Vectors |
Lesson #3 |

**A) Your Mission: Plan a flight from your state capital to Chicago, Illinois with a stop over in St. Louis, Missouri.**

- Locate a map of the U.S. (Try the Reference Material section for online maps.) Find your state capital on the map.
- Draw a vector from your state capital to St. Louis. Using a ruler, compass rose or protractor, and the map, determine the flight's:
- a) Distance (km)
- b) Directional heading in degrees (as measured from 0º North)
- c) Displacement

- Draw another vector from St. Louis to Chicago. Again using a ruler, compass rose or protractor, and the map, determine this flight's:
- a) Distance (km)
- b) Directional heading in degrees (as measured from 0º North)
- c) Displacement

- Check your displacements using the How Far Is It? web site for each leg of the flight.
- a) Displacement from state capital to St. Louis (km and degrees)
- b) Displacement from St. Louis to Chicago (km and degrees)

**B) How far has the plane traveled?**

- Find the total distance the plane traveled by adding the distance that each vector represents.
- Does this value indicate how far the final destination is from the origin?

**C) How far is the plane from your state capital at the end of the trip?**

The value that you are looking for is the total displacement which is the distance **and** direction from the point of origin to your final destination. To determine this you must add the vectors:

**Vector Addition Instructions**

- Draw the first vector on your map (your state capital to St. Louis).
- Draw the second vector on your map (St. Louis to Chicago) with the tail of this vector beginning at the head of the first vector.
- Draw a third vector called the resultant from the tail of the first vector to the head of the second vector.
- Measure the length of the resultant vector (km) and its directional heading (degrees) from your state capital. This resultant represents the total displacement of the plane.

- What is the resultant displacement of the plane from your state capital to Chicago (as measured from your vector diagram)?
- How did your measured displacement compare with the displacement found using the How Far Is It? web site?
- Do your results make sense? Why or why not?

**D) Ready to become a Pilot?**

- Think of a situation (other than flying) where it would be preferable to know displacement rather than distance traveled.
- Think of a situation (other than flying) where it would be preferable to know distance traveled rather than displacement.
- Demonstrate how a magnetic compass could be used to find the displacement of a hiker.
- Create a vector game or puzzle for your classmates to solve. It could be a board game, a maze, a riddle, a mystery, a treasure hunt or anything else that you wish. It should use 5 vectors. Trade games/puzzles with your classmates and see if they solve it correctly.