Lesson 14: Vectors in Two Dimensions
Two dimensional problems are a little tougher, because we are no longer just lining up collinear vectors
and doing quick math.
●
Instead, we need to pay attention to how the vectors form a more complex (but not very
complex) diagram. The majority of these diagrams will involve right angle triangles.
●
If they are right angle triangles, just use your regular trig (SOH CAH TOA) and
pythagoras (c
2
= a
2
+ b
2
).
●
You'll want to be thinking about
physics
as you set up your diagram (so that you get everything
pointing headtotail and stuff) and then switch over to doing
math
just like any trig problem.
Components of Vectors
One of the most important ideas in vectors is components.
●
Just like a component stereo system is made of several individual parts working together,
components of vectors
are the individual parts that add up to the overall
resultant
.
Example 1
: A car drives
10km [E]
and then
7 km [N]
. Determine its displacement.
First, draw a proper diagram:
The
red
and the
blue
vectors are the components of the resultant.
●
The
red
and
blue
components show you how walking
East
and the
North
will result in
you moving more or less in a NorthEast direction.
Notice how this diagram even shows the vectors being added in the correct order according to
the question.
●
10 km [E]
is shown leading up to
7.0 km [N]
. Start at the tail of the red arrow and
follow the path it takes you along. You eventually end up at the head of the blue vector.
●
If you added them with
7.0 km [N]
and then
10 km [E]
you would still get the same
final answer, just with a different angle because of a different reference point.
●
The resultant is drawn in headtohead and tailtotail, just like a resultant is always
supposed to be.
This is certainly a right angle triangle, so just use c
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 Fall '08
 Staff
 Cartesian Coordinate System, Two Dimensions, Cartesian Method, navigator method

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