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Vector addition problem

  1. Sep 29, 2008 #1
    The Problem:
    A car is driven 175 km west and then 80 km southwest (45°). What is the displacement of the car from the point of origin (magnitude and direction)?

    I have drawn myself a diagram, and I know you need to use the angles to help decide how much displacement, but I don't know how to use them.

    It seems like whenever I get the distance of each vector I can just add those two and it will give me total displacement.

    How can I use the distances 175 and 80 with the angles 0 deg. and 45 deg., respectively, to find the total displacement? Is there some sort of equation I'm missing?

    Thanks in advance...

    Wade
     
  2. jcsd
  3. Sep 29, 2008 #2

    LowlyPion

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    If you describe your vectors as x and y components the components may be added together to determine your resultant.
    At that point let Pythagoras be your guide.
     
  4. Sep 29, 2008 #3

    I'm not sure I know what you mean? What is X and what is Y? and I still don't get where the angles fit in here...
     
  5. Sep 29, 2008 #4

    LowlyPion

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    They can be whatever you want. I would choose East and North. The only real requirement is that they be orthogonal.
     
  6. Sep 29, 2008 #5
    ok well I did cos (45)= (x/80) and solved for x to get 42.026. then I added that to 175 to get 217.026 for the final x-component (km). Is this correct or close? My homework says it is wrong, but I can't see why?
     
  7. Sep 29, 2008 #6
    nobody?
     
  8. Sep 29, 2008 #7

    LowlyPion

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    What about the y component?
     
  9. Sep 29, 2008 #8
    well I did sin(45)=(y/80), and got 56.569. This answer is also wrong according to the computer.

    Can you or anyone please explain why?
     
  10. Sep 29, 2008 #9
    bump...
     
  11. Sep 29, 2008 #10
    anybody please... it's due in like 15 minutes...
     
  12. Sep 29, 2008 #11

    LowlyPion

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    OK you have now the X- component and the Y component use the Pythagorean theorem to solve for the magnitude.

    Then figure the angle from sin or cos.
     
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