Example 1
You walk 15m at 35 West of South. How far West and how far South did you walk?

dx
Need an angle inside of the vector diagram.
90  35  55
55

dy
35

15 m  d

dd
cos 55  x x
15 m

d x  15 m cos 55

d x  8.6 m West

dd
sin 55  y y
15 m

d y  15 m sin 55

d y  12 m South
Resolving Vectors into their Perpendicular Components
Example 1
You walk 15m at 35 West of South. How far West and how far South did you walk?

dx
55

dy
35

15 m  d

d
cos 55  x
15 m

d x  15 m cos 55

d x  8.6 m West
Components – The two vectors that are added to
give the resultant
Perpendicular Components – Components that
are perpendicular
 Perpendicular components are
independent of one another

d
sin 55  y
15 m

d y  15 m sin 55

d y  12 m South
To resolve a vector into its perpendicular components
1. Draw the resultant.
2. Draw the horizontal component starting at the tail of the resultant.
3. Draw the vertical component starting at the head of the horizontal
component.

dx

dy
35

15 m  d
Resolving Vectors into their Perpendicular Components
Example 2
Resolve a 50. m velocity at 120. into its perpendicular components.
s

vy

50. m  v
s
120

vx
Resolving Vectors into their Perpendicular Components
Example 2
Resolve a 50. m velocity at 120. into its perpendicular components.
s
Need an angle inside of the vector diagram.
180.  120.  60.

vy
 
vx vx
cos 60. 
50. m

50. m  v
s

vx
60.
s

vx  50. m cos 60.
s

mm
vx  25
25
s s
Need a direction.
120

vx
cos120. 
50. m
 
vy vy
sin 120. 
50. m
s
s

vx  50. m cos120.
s

v y  50. m sin 120.
s

vx  25 m

v y  43 m
s
s
Notice that positive means
up.
Resolving Vectors into their Perpendicular Components
Example 2
Resolve a 50. m velocity at 120. into its perpendicular components.
s
To determine +/1. Look at the direction of the vector.

vy

50. m  v
s

vx
60.
120
2. Examine the quadrant in which the
vector is drawn.
3. Use the angle measured from the
positive horizontal.
 Must draw the horizontal
component first!