Pointing the Way Vectors

Representing Vectors Vectors are represented on paper by arrows Direction = WAY THE ARROW POINTS Magnitude = ARROW LENGTH Examples of Vectors Displacement Velocity Acceleration

Angular Systems Reference Vector Compass Point System Uses due EAST as the 0 degree reference, all other angles are measured from that point 20 meters at 190° 34 meters at 48° Compass Point System Uses angles measured from various compass points to reference vector direction 20 meters at 10° south of west 34 meters at 42° east of north 90° N 180° W E 0° 270° S

Changing Systems What is the reference vector angle for a vector that points 50 degrees east of south? What is the reference vector angle for a vector that points 20 degrees north of east? 50° 270° + 50° = 320° 20° 20°

Adding Vectors Graphically

Vector Components Break vector into two perpendicular components using X-Y system AX = A cos θ AY = A sin θ Example v = 6.0 m/s at 30° vx = 6.0 m/s (cos 30°) = 5.2 m/s vy = 6.0 m/s (sin 30°) = 3.0 m/s 6.0 m/s vY 30° vX

Adding Vectors Using Components Vectors can be added together by adding their COMPONENTS Results are used to find RESULTANT MAGNITUDE RESULTANT DIRECTION