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Homework Help: Grade 12, Vector Addition

  1. Sep 15, 2011 #1
    1. The problem statement, all variables and given/known data
    A plane heads 20° north of east at 200 m/s. The wind blows 60° north of east at 50 m/s. What is the resultant velocity of the plane?


    2. Relevant equations
    Δv= v2-v1 or Δv= v2+(-v1)


    3. The attempt at a solution
    I know you have to solve for the x and y, but I don't know how to do that. Then I know once you get your two answers, you use pythagorean theorem to get the final answer.
     
  2. jcsd
  3. Sep 15, 2011 #2

    gb7nash

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    First off, every vector in 2D has an x component and a y component. How do you find the x and y component for a given vector?
     
  4. Sep 15, 2011 #3
    You use sinΘ or cosΘ, and then you times that number by the velocity.
     
  5. Sep 15, 2011 #4

    gb7nash

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    Ok...so do it and show what the x and y components are of the plane and the wind.
     
  6. Sep 15, 2011 #5
    Once you get what he says add the x components and y components vectorally.
     
  7. Sep 15, 2011 #6
    So my total for x was 111 and for y it was 213. So then I used pythagorean theorem and got 240. I'm not sure if this is correct though. And then for my angle i got 62.5
     
  8. Sep 15, 2011 #7

    gb7nash

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    You got your sin and cos mixed up. x = rcosΘ and y = rsinΘ. Besides that, do what you were doing.

    Also, in the future, show your work. I'm lucky to have a calculator handy, so I can tell where you made your mistake, but it's easier to follow your work than trying to decipher what you did.
     
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