Chap. 3: Kinematics in Two or Three Dimensions: Vectors Study guide is posted online (Homework page)

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.]

Problem 6

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

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

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

Problem 16 16. (III) You are given a vector in the xy plane that has a magnitude of 90.0 units and a y component of -55units (a) What are the two possibilities for its x component? (b) Assuming the x component is known to be positive, specify the vector which, if you add it to the original one, would give a resultant vector that is 80.0 units long and points entirely in the -x direction.

Adding Vectors by Components Example 3-2: Mail carrier’s displacement. A rural mail carrier leaves the post office and drives 22.0 km in a northerly direction. She then drives in a direction 60.0° south of east for 47.0 km. What is her displacement from the post office?

Vector Kinematics In two or three dimensions, the displacement is a vector: