1. Vector Quantities Vectors have ▫magnitude ▫direction Physical vector quantities ▫displacement ▫velocity ▫acceleration ▫force

2. Coordinate System Cartesian Coordinates ▫Rectangular ▫(x,y) ▫Angles start on positive x-axis 180º (W) 90º (N) 0º (E) 270º (S)

3. Representing Vectors Magnitude (Size) ▫length of vector is proportional to magnitude ▫choose a scale that fits the problem  1.0 cm = 10 m/s or 1.0 cm = 1 m/s Direction (Angle or Sign) ▫Point vector in direction of quantity  North, South, East, West  Degrees above positive x-axis

4. Vector Addition Vectors in one direction ▫direction is analogous to sign ▫add quantities in same direction ▫subtract quantities in opposite direction ▫sum is called resultant R = A + B BA A B

5. Vector Addition in Two Dimensions A B R=A+B Tip to Tail Method of Vector Addition

6. Vector Addition in Two Dimensions Parallelogram Method Rule: Always put an arrowhead on vectors! 1.Draw both vectors, beginning at the origin. 2.Draw a vector parallel to A beginning at the tip of B. Keep length of new vector equal to A. 3.Draw a vector parallel to B beginning at the tip of A. Keep length of new vector equal to B. 4.Draw the resultant along the diagonal of the parallelogram, beginning at the origin. 5.Measure the magnitude and angle of the resultant.

7. Vector Addition in Two Dimensions Parallelogram Method A B R=A+B

8. Adding Multiple Vectors Use tip-to-tail method. Draw third vector beginning at the tip of the second vector. Continue for additional vectors. Resultant is drawn from the tail of the first vector to the tip of the last vector.

9. Sally walked 3 block north, and then 4 blocks east. What is her displacement?