Question 540874: The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 1850, bearing 125°
v: magnitude 2960, bearing 25°
w: u + 2v
I am having a hard time can you please help
thanks bunches
Found 2 solutions by scott8148, KMST:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! Ux = 1850 * cos(125º) ___ Uy = 1850 * sin(125º)
Vx = 2960 * cos(25º) ___ Vy = 2960 * sin(25º)
Wx = Ux + Vx ___ Wy = Uy + Vy
the tangent of the bearing angle is ___ Wy / Wx
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! I saw two ways to deal with the problem. I calculated it both ways to find and diagnose errors in the calculations. (I usually make calculations mistakes (and I did this time), but I always find them and correct them. Embarrassing typos, however, are another story).
The way I like best is going from polar to rectangular coordinates before adding the vectors, and transforming the result into polar coordinates. I think that's what you would be expected to do, and I find it easier.
All calculations are based on the very accurate and precise (but not exact) values for trigonometric functions from my calculator.
u has  , 
v has  , 
In rectangular coordinates (in matrix form):
or maybe you use this notation:
 
(or equivalent in whatever notation you use)
Back to polar coordinates:
and  --> 
are the polar coordinates for u+2v: magnitude 5887.725395, bearing 43.02545°
(I do not think too many digits are required for the answer, probably the expected answer is magnitude 5888, bearing 43°).
Another approach, using geometry and trigonometry, would involve a triangle with sides representing vectors u and 2v.
One side would have a length of 5920, and would form a 25° angle with the horizontal.
The other side would have a length of 1850, and would form a 125° angle with the horizontal.
The third side of the triangle represents u+2v.
You calculate the angle of the two known sides as 80°.
Then you could use law of cosines to calculate the length of the third side, which is the magnitude of u+2v, as:
After that, you could use law of sines to fins another angle of the triangle. For example, the angle (A) opposed to the side with length 1850, could be calculated from
 -->  --> A=18.02545072
Finally, that angle (between vectors 2v and u+2v) would have to be added to the 25° angle between the x axis and v (or 2v), to give the angle between the x axis and u+2v, so
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