Solving vectors using component method

  1. 1. The problem statement, all variables and given/known data
    Add the following vectors using component method:
    Vector A=175km; 30 degrees north of east
    Vector B=153km; 20 degrees west of north
    Vector C=195km; West
    a)Find x and y component of each vector
    b)Solve for the magnitude of resultant vector
    c) Solve for direction(angle)

    2. The attempt at a solution
    So i these are what i got
    Vector A: x=175cos 30....x=151.56 y=175sin 30......y=87.5
    Vector B: x=153cos 20....x=-143.77 y=153sin 20.....y=52.33
    (are these correct?)
    so after getting this i added all the x's and y's but then i realized that the question had said that vector C goes 195km west, so i now got confused what to do next.

    please help thank you for your time.
     
  2. jcsd
  3. NascentOxygen

    Staff: Mentor

    There is nothing special about "in a westerly direction". A westerly vector contributes a component D.cos 180o in the x-direction, and D.sin 0o in the y-direction.
     
  4. well that was stupid of me, thanks for the reply finally solved it :D
     
  5. HallsofIvy

    HallsofIvy 40,795
    Staff Emeritus
    Science Advisor

    If [itex]\theta[/itex] is measured counterclockwise from the positive x-axis then a vector of length r and angle [itex]\theta[/itex] has components [itex]rcos(\theta)[/itex] and [itex]r sin(\theta)[/itex]. Strictly speaking, you are free to choose the "positive x-axis" any way you want as long as you are consistent but the usual convention is that the positive x-axis points East.

    For the first vector you are given that r= 175km and the directon is 30 degrees north of east. "north of east" is counterclockwise from east so the angle is [itex]\theta= 30[/itex] degrees.

    For the second vector you are given that r= 153km and the direction is 20 degrees west of north. West is clockwise of north but north itself is 90 degrees clockwise of east. The angle is [itex]\theta= 90+20= 110[/itex] degrees.

    For the third vector you are given that r= 195km and the direction is west. West is exactly opposite east so the angle is [itex]\theta= 180[/itex] degrees.
     
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