The document discusses breaking vectors into perpendicular components. It provides an example of resolving a displacement vector of Janice walking 10 km northeast, then 4 km west, and 1.9 km north into its east and north components. The total displacement is calculated to be 3.1 km east and 9 km north, for a total displacement of 9.5 km in a northeast direction. Practice problems are provided to reinforce working with vector components.

1. Vector Components
 Break, or Resolve, a Vector intoBreak, or Resolve, a Vector into
Two Perpendicular ComponentsTwo Perpendicular Components
Nelson Reference Pages:Nelson Reference Pages:
Pages 66 - 70Pages 66 - 70

2.  Like forces, all vectors can be broken into twoLike forces, all vectors can be broken into two ⊥⊥
components.components.
 Example:Example: Janice walks 10.0 km [NE], then 4.0 km [W], andJanice walks 10.0 km [NE], then 4.0 km [W], and
finally walks 1.9 km [N]. Determine Janice’s totalfinally walks 1.9 km [N]. Determine Janice’s total
displacement.displacement.
Solution:Solution: Below, the 10.0 km displacement vector is brokenBelow, the 10.0 km displacement vector is broken
(or “(or “resolvedresolved”) into two”) into two ⊥⊥ components which are then addedcomponents which are then added
to the other vectors.to the other vectors.
 ΔΔdd TotalTotal = 7.1 km [E] + 4.0 km [W] + 7.1 km [N] + 1.9 km [N]= 7.1 km [E] + 4.0 km [W] + 7.1 km [N] + 1.9 km [N]
= 7.1 km [E] - 4.0 km [E] + 7.1 km [N] + 1.9 km [N]= 7.1 km [E] - 4.0 km [E] + 7.1 km [N] + 1.9 km [N]
= 3.1 km [E] + 9.0 km [N]= 3.1 km [E] + 9.0 km [N]
1 0 . 0 k m
1 0 . 0 ( c o s 4 5 ) k m =
7 . 1 k m
10.0(sin45)km=
7.1km N
W E

3. The two components mustThe two components must
be added and this isbe added and this is
shown in the diagram.shown in the diagram.
The angle is calculated asThe angle is calculated as
TanTan-1-1
(9.0/3.1) = 71(9.0/3.1) = 7100
Δd Total = 9.5 km [E 710
N]
3 .1 k m
9.0km
N
W E
dTotal=9.5km

4. Practice Questions
Nelson TB:
 Page 75 # 1, 2, 3Page 75 # 1, 2, 3 (for # 2 & 3 use components)
 Page 75 #7Page 75 #7
(Ensure you are comfortable adding components from 3, 4
or more vectors)
Go to lesson 5 (scaled vector diagrams), of Kinematics
Unit, and redo the following problem using components.
“A boat heads from port…”