In a vector problem, what does 30 degrees north of west mean? How would I find the x and y component given a force of 30N for the vector?

- anonymous

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- phi

30 degrees north of west means face west and then turn 30º towards the north

- anonymous

That makes sense! How would I find the x and y components?

- phi

First, you have to define your x and y axes, what is 0º and what direction do you turn to face 90º.... In algebra, the 0º is the angle from the x-axis, and you turn counter clockwise to get to 90º (the y-axis)
but if you use the compass directions, 0º (north) is the y axis, and you turn CLOCKWISE 90º to get to the x-axis (east)
which convention are you using ?

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- anonymous

The latter

- phi

|dw:1380674698896:dw|

- anonymous

That's actually a good point, because I am sort of confused... In an example the worksheet says the velocity is due east, and the velocity is from the south but the diagram is like this:|dw:1380674786945:dw|

- phi

the length of the vector is 30N

- anonymous

the arrow pointing to the left is labeled as plane velocity, and the arrow pointing up is labeled as wind velocity...

- anonymous

But Im confused because isnt the plane's velocity due east? Why is it towards the left?

- anonymous

|dw:1380674949407:dw|

- anonymous

Is the convention different? Am I confusing them?

- phi

can you post the example? Sometimes when they say an easterly wind, they mean the wind comes from the east and goes west.

- anonymous

Okay, so the example states that a plane takes off from an airport. Its velocity is 550 mph due east. There is wind blowing with a velocity of 150 mph from the south.
The drawing they provide for the information:
|dw:1380675268151:dw|

- anonymous

|dw:1380675429557:dw|

- anonymous

The pythagorean theorem is used to find the magnitude, but there's a word of caution for finding the "direction of the jet's velocity vector measured east of north": they say that the angle is being measured from the y-axis toward the negative x-axis, which means the x component is the side opposite theta and the y component is adj to the theta. I'm confused.

- phi

That picture is "non-standard" east never points to the left.
but if we assume the plane is going east, and the wind is from the south, the vector will be going north and east... we just need the exact angle.
it would be going x degrees north of east where x = stan(150/550)
or xx degrees east of north where xx= stan(550/150)

- phi

*atan not stan (spell checker keeps "fixing" it)

- anonymous

I'm sort of lost.... so which of the two conventions should I be using?

- anonymous

I've been doing counter clockwise from the x axis

- phi

***they say that the angle is being measured from the y-axis toward the negative x-axis, which means the x component is the side opposite theta and the y component is adj to the theta.****
they are saying what this picture shows
|dw:1380675769367:dw|

- anonymous

Ohhh okay. So i have to flip the two given magnitudes.

- phi

no, you don't flip anything
|dw:1380675897367:dw|

- anonymous

Going back to the original question (30N, 30 degrees north of west): I drew the vector like so.... |dw:1380675900561:dw|????

- anonymous

And that makes sense about that I don't have to flip it

- phi

I would stick with the convention
N 0º East 90º
and do it the way I posted it
|dw:1380676059095:dw|

- anonymous

So.... How should I be drawing that vector?

- phi

? It is drawn... the only thing left out is r is 30N

- anonymous

So for 30 degrees north of west, I need to go 30 degrees counter clockwise from 0/North?

- anonymous

So basically north of west means northwest?

- phi

northwest means specifically 45º north of west
***So for 30 degrees north of west, I need to go 30 degrees counter clockwise from 0/North? ***
no, you start at west and turn 30º toward north. On a compass you would be have a heading of 300º (and 360º is north)

- anonymous

Oh okay! So, for an example west of south 10 degrees means to start at 270 degrees, and then go towards south or 180 degrees by 10? So I would have a heading of 260?

- anonymous

|dw:1380676506453:dw|

- phi

for an example west of south 10 degrees means
means you are 10º west of SOUTH. you are at 180, and then turn 10º towards the west (as opposed to the east). you will be looking 190º

- anonymous

Got it, so one more example. 15 degrees south of east say means start at 90 degrees (east) and go towards the south by 15 degrees. So I would have a heading of 105?

- phi

yes. In English we say things like " I was standing 10 feet south of the tree"
the phrase "of the tree" is the starting point... and then we change our position relative to that starting position
it works the same for angles. 15 degrees south of east
the "of east" is the starting point. then we adjust our direction by 15 degrees (turning towards the south)

- anonymous

That makes so much more sense! As for that example, you said it was non-standard?

- phi

yes, see https://en.wikipedia.org/wiki/Cardinal_direction
North is up, East is to the right

- anonymous

Great! Thank you so much for the help! I should question my TA at recitation about that, haha! :)

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