1. Pointing the Way
Vectors

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

3. 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

4. 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°

5. Adding Vectors Graphically

6. 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

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