1. Chap. 3: Kinematics in Two or Three Dimensions: Vectors
HW3: Chap. 2: Pb. 51, Pb. 63, Pb. 67;
Chap 3:Pb.3,Pb.5, Pb.10, Pb.38, Pb.46
Due Wed, Sept. 12
Study guide is posted online (Homework page)

2. Vector Addition: Components
If the components are perpendicular, they can be found using trigonometric functions.

3. Vector Addition: Components
We don’t always carry around a ruler and a protractor, and our result isn’t always very precise even when we do. In this course we will use components to add vectors.
However, you should still always draw the vector addition to help you visualize the situation.
What are components here?
Parts of the vector that lie on the coordinate axes y Ay A x Ax

4. Vector Addition: Components
Once we have the components of C, Cx and Cy, we can find the magnitude and direction of C.
magnitude Cx Cy C
South of East
direction

5. Problem 5
5. (II) V is a vector 24.8 units in magnitude and points at an angle of 23.4° above the negative x axis. (a) Sketch this vector. (b) Calculate Vx and Vy (c) Use Vx and Vy to obtain (again) the magnitude and direction of V [Note: Part (c) is a good way to check if you’ve resolved your vector correctly.]

6. Problem 6

7. Vector Addition: Components
We add vectors by adding their x and y components because we can add things in a line y x y B A By Ay Ax x Bx A B By Ay Ax C C Bx

8. Vector Addition: Components
We add vectors by adding their x and y components. By Ay Ax Bx C Bx Ax Cx Ay By Cx C Cy Cy

9. Vector Addition: Components
Once we have the components of C, Cx and Cy, we can find the magnitude and direction of C.
magnitude Cx Cy C
South of East
direction

10. Unit Vectors Unit vectors have magnitude 1.
Using unit vectors, any vector can be written in terms of its components:

11. Problem 10
10. (II) Three vectors are shown in Fig. 3–38. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with x axis.