1. Vectors

2. Adding Vectors += Resultant

3. Adding Vectors += Resultant +=

4. Adding Vectors (now with numbers!) += 4 m East3 m North 4 m 3 m r = 5 m

5. Adding Vectors (now with numbers!) += 4 m East3 m North 4 m 3 m r = 5 m θ Make sure your calculator is in DEGREES mode!!!!!!

6. Measuring Angles Measure ALL angles starting from the positive x-axis! +y II 180-θ 90-180 o I θ 0-90 o III 180+θ 180-270 o IV 360-θ 270-360 o +x -x -y

7. Vector Components x-component y-component θ Vectors are made up two components: x & y

8. Vector Components x-component = r x y-component = r y θ r

9. Adding Multiple Vectors Find x & y components of each vector Add all x’s to get final x component Add all y’s to get final y component Pythagorean theorem tan -1

10. Relative Velocity If two objects are moving towards or away from each other, depending on your reference point, the velocity may appear to be different (relative velocity)

11. Boat Problems To measure “relative to shore”, measure the angle between the shore and the resultant θ θ