mr.p: Good morning, today we're going to learn
how to use cardinal directions with vectors.
Here we go.
Bo: Hey guys.
Billy: Hey Bo. Bobby: Hi Bo.
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mr.p: In our previous lesson we did an example where
we added two velocity vectors A and B together
to get the resultant velocity vector R
of our slow velocity racer.
Our answer was 65 millimeters per second
at an angle of 41 degrees east of north.
Today we're going to learn why
this angle theta is east of north.
Bo: Thanks.
Billy: Agreed.
mr.p: However, before we do I need to remind
you that I am spelling impaired.
It is really difficult for me to spell words.
Bobby: No, he really can't spell.
mr.p: Yep. I have a really hard time spelling.
I admit it and I work with it.
Some of you need to admit that
you are directionally impaired.
Bo: Pfft I'm not directionally impaired.
mr.p: Yes a lot of students struggle with cardinal directions.
Because of your possible directional
impairment I have two suggestions.
One, always draw this compass rose on any sheet
of paper where you are working with cardinal directions,
just like this only smaller.
Second, never turn the sheet of
paper that you're working with.
Always keep it oriented vertically.
The moment you begin to turn your paper we all get confused.
mr.p: Because it's confusing if north is
not always forward relative to you.
Now let's talk about how I identify this angle
here theta of 41 degrees to be east of north.
So this angle right here is angle theta east of north.
Same theta and also east of north.
I've also drawn a small compass rose on the tail
of our resultant vector R, which is something
that I do suggest that you do if you
are struggling with cardinal directions.
I do think that people find it easier rather than
thinking of it as "of", but rather "from" beacuse
that's what the "of" means in this particular case.
This angle theta is 41 degrees east from north.
In other words, you're moving the direction of east
from the northward direction, eastward from north.
Billy, what then is the direction of this angle?
Billy: That would be north of east.
mr.p: Correct, this angle is north of east.
And Bobby how should we describe this angle?
Bobby: Uh west from north, west of north.
mr.p: Correct, this angle is west from north.
And Bo what about this angle?
Bo: South of west.
mr.p: Correct, this angle is south of west.
We're moving southward from west.
And Bobby how would we describe this angle?
Bobby: North of south.
mr.p: Bobby actually north of south doesn't work.
This direction would be north of south,
but this direction also would be northward from south,
so that doesn't really work.
So Bobby please try again.
Bobby: Uh yeah sorry, umm west of south.
mr.p: There you go Bobby, yes that is west of south.
Bo how about this one?
Bo: That's north of west.
mr.p: Yes that is north of west or northward from west.
And Bobby what about this angle?
Bobby: South of east.
mr.p: Correct this is southward from east or south of east.
And Billy how about this last one?
Billy: Uh that one is east of south.
mr.p: Yes the last direction is east of south.
And you can now see on the board in red are eight
options for describing the direction of
an angle using cardinal directions.
Now let's return back to our original resultant
vector which was 65 millimeteres per second
at an angle of 41 degrees east of north.
There is actually a second, equivalent way
to describe the direction of this resultant vector.
We could describe this resultant vector
with what other equivalent angle?
Bobby: Oh uh it's 49 degrees north of east.
mr.p: Correct, we could also describe this
vector as 65 millimeters per second
at an angle of 49 degrees north of east.
And Bobby how did you get 49 degrees?
Bobby: Well 41 and 49 degrees are complementary angles.
Bo: What do you mean complementary angles?
Bobby: Uh they add up to 90 degrees. Bo: Oh yeah.
mr.p: Correct, north and east are 90 degrees relative
to one another, therefore these two angles
are going to be complementary to one another,
therefore this angle right here is
going to be 90 minus 41 degrees.
One other small thing, sometimes
you'll see NE, SE, SW, or NW.
They mean northeast, southeast, southwest, and northwest.
And they mean actually a specific direction.
So it means exactly 45 degrees between the two directions.
Billy: Uh so then northeast could be 45 degrees east
of north or 45 degrees north of east.
mr.p: Correct, but generally people will write SW
for example rather than 45 degrees south of west.
Let's do a quick review.
Please always draw a compass rose on your sheet of paper
whenever working with cardinal directions.
If you're having issues it's always good too to
draw a small compass rose of the tail of any
vector you're trying to figure out the angle of.
We have our eight choices for our cardinal directions
and rather than east of north it's actually easier
to think of it as east from north.
In other words, eastward from north.
Oh and don't forget your complementary angles.
Thank you very much for learning with me today.
I enjoyed learning with you.