Solving Vector Question: Finding rAB Coordinates | TunerSpec.ca

[ThomasHW]

Homework Statement

http://www.tunerspec.ca/school/question7.jpg

The Attempt at a Solution

Not sure where to start. I want to get the x & y coordinates of rAB but I'm not sure how.

 

[learningphysics]

Get the angle of vector OB from the positive x - axis going counterclockwise...

 

[ThomasHW]

How?

 

[learningphysics]

How?

Can you get the angle of OA from the positive x-axis?

 

[ThomasHW]

Using

tan x = \frac{711j}{418i}

x = 59.55^{\circ}

 

[learningphysics]

Using

tan x = \frac{711j}{418i}

x = 59.55^{\circ}

good. what's the relationship between that OA and angle... and the OB angle?

 

[ThomasHW]

I'm not sure...

If this ends up being easy I'm going to feel stupid.

 

[dontdisturbmycircles]

Label the angle which is 59.55*. You have a triangle and 3 sides are known, use the cosine law to determine any angle right? From that you can get the angle that |r_{oa}+r_{ab}| makes with the origin.

Then you can use the angle and sine/cosine to find the coords of the point B or you can set up a unit vector and multiply by the magnitude of the |r_{oa}+r_{ab}| to get the components.

 

[learningphysics]

I'm not sure...

If this ends up being easy I'm going to feel stupid.

Oops... I thought I posted a reply. Sorry about that!

Use the angle AOB, and subtract it away from the angle of OA... that gives the angle of OB...

 

[ThomasHW]

I'm getting a length of 824.77m for side OA. It looks too big according to the diagram, is it right?

Assuming it is...

I used the cosine law to determine the angle for AOB (43.99) and subtracted that from angle x (determined previously.) This gave me an angle of 15.56 from the x-axis to OB. Then using the length of 606m and the angle of 15.56 I determined the x and y coordinates to be 583.79m and 162.56m, respectively.

Is that right?

 

[learningphysics]

I'm getting a length of 824.77m for side OA. It looks too big according to the diagram, is it right?

Assuming it is...

I used the cosine law to determine the angle for AOB (43.99) and subtracted that from angle x (determined previously.) This gave me an angle of 15.56 from the x-axis to OB. Then using the length of 606m and the angle of 15.56 I determined the x and y coordinates to be 583.79m and 162.56m, respectively.

Is that right?

yup. looks right to me.

 

[ThomasHW]

Thank you for the help. :)