Vector Addition – Graphical Method
Example
You walk 75 m West then 50. m South, what is your displacement?
Scale
What would a 75 m West displacement look like?
1.0 cm = 5.0 m
15 cm = 75 m
Pointing West (Left)
75 m
Vector Addition – Graphical Method
Example
You walk 75 m West then 50. m South, what is your displacement?
Scale
1.0 cm = 5.0 m
What would a 50. m South displacement look like?
10. cm = 50. m
Pointing South (Down)
75 m
50. m
Vector Addition – Graphical Method
Example
You walk 75 m West then 50. m South, what is your displacement?
Scale
How could we represent your displacement over the entire trip?
1.0 cm = 5.0 m
18.0 cm = 90.0 m
75 m
50. m
Vector Addition – Graphical Method
Example
You walk 75 m West then 50. m South, what is your displacement?
Scale
1.0 cm = 5.0 m
18.0 cm = 90.0 m
75 m
50. m
90.0 m
Vector Addition – Graphical Method
Example
You walk 75 m West then 50. m South, what is your displacement?
Scale
1.0 cm = 5.0 m
18.0 cm = 90.0 m
75 m
34°
50. m
90.0 m

d  Displaceme nt

d  90.0 m at 34 S of W
Resultant – the one vector whose effect on a body is the same as the
net effect of two or more other vectors.
Vector Addition – Graphical Method
Example
What would your displacement be if you walked South and then West?

a
75 m
50. m

b

d
  90 - 34
  56

50. m

d  90.0 m at 56 W of S
75 m
    
d a b b a
Vector addition is Commutative!
Vector Addition – Graphical Method
To find a resultant using the graphical method
1. Draw one vector to scale.
 Draw the horizontal vector first when possible.
2. Draw the second vector to the same scale, placing the tail of
the second at the head of the first.
 Head-to-tail construction is the graphical representation of vector addition!
3. Draw the resultant vector from the tail of the first vector to the
head of the last.
75 m

50. m

d