Components of Vectors

1. Components of Vectors 4.2

2. The basics… • In the last section, we dealt with two vectors in the same direction, opposite directions, and at right angles to each other. • In this section we will deal with one vector, and try to figure out the other two sides of the triangle.

3. Problem Solving Steps • 1. draw a coordinate system (a graph) • 2. choose the correct formula • 3. plug in your numbers (calculator must be in degree mode!) • 4. check to see if your answer needs a negative sign (what quadrant is your vector in?)

4. The formulas: • For the X side use Ax = Acosθ • For the Y side use Ay = Asinθ

5. Example 1 • Draw a vector of a car that travels 60 km to the northwest

6. Example 2 • Draw a vector representing a football being thrown 30 m south of east at a 60° angle (that’s physics speak for southeast)

7. 60°

8. One more thing… • When you are given a direction to draw your vector, simply follow the directions; north of east, south of east, north of west or south of west.

9. If you are only given an angle, start measuring your angle from the positive x axis and move counterclockwise.

10. Important! • The angle you use in a calculation is always the angle INSIDE the triangle you formed

11. Example3 • Draw a picture showing a golf ball being hit at an angle of 110° • Answer?...

13. Putting it all together • What are the components of a vector of magnitude 5.6 m at an angle of 47° from the positive x axis?

14. 1. Draw a picture 47°

15. 2. Choose the correct formula • Because “solving for the components” means what are the x and y sides of my triangle, I will use Ax = Acosθ for the x side, and Ay = Asinθ for the y side • Here’s how this looks… • Ax = 5.6cos47 ( Ax = 3.82m) • Ay = 5.6sin47 (Ay = 4.09m)

16. 3. Do you need to add a negative sign? • Since the original vector is in quadrant 1, no.

18. Classwork/homework • P. 74 #’s 11-14 • P. 79 #’s 25, 26, 27a, 29 (use graph paper or be very careful!) and 30

19. Physics is fun!!