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Magnitude and direction

  1. Sep 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Orv walks 312 m due east. He then continues walking along a straight line, but in a different direction, and stops 220 m northeast of his starting point. How far did he walk during the second portion of the trip and in what direction?
    What is the magnitude?
    What is the direction ___________ ° counterclockwise from the +x-axis



    2. Relevant equations
    C=squareroot of 312^2+220^2
    What equation to use to find direction??

    3. The attempt at a solution
    C= Magnitude= 381.76 m why is my magnitude wrong?
     
  2. jcsd
  3. Sep 15, 2011 #2
    A good idea here is to read the problem carefully, and/or make a simple diagram.
    You're correct in using the Pythagorean theorem for this problem, but you're using it incorrectly. Remember that the form is a^2 + b^2 = c^2, where c is the hypotenuse.

    In the problem statement, you're given a = 312 meters (The distance walked east -- one of the legs of the triangle), and c = 220 meters (The distance in a straight line from the starting point -- the hypotenuse).

    This means that what you need to find here is b, not c.
     
  4. Sep 15, 2011 #3
    As with regards to your direction issues, once you have your three sides figured out, use your trig laws (soh cah toa).

    If you've never heard of them, it goes:
    "soh" - sin = opposite / hypotenuse
    "cah" - cosine = adjacent / hypotenuse
    "toa" - tangent = opposite / adjacent

    And you should get the right answer.
    Cheers

    EDIT: or your sin/cosine laws. I didn't work through the problem myself, I just assumed based on the level it was a right angle triangle.
     
  5. Sep 15, 2011 #4
    Same. Now that I look at it (through my sleepy eyes), the 'hypotenuse' is shorter than one of the legs, and by a good bit, too...
     
  6. Sep 16, 2011 #5
    I cant take the square root of a negative number for the magnitude... Is there another way to solve this...
     
  7. Sep 16, 2011 #6
    Did you ever draw it?
     

    Attached Files:

  8. Sep 17, 2011 #7
    @:AC130NAV: The problem states that the final position was 220 m from the starting point in an north easterly direction, so your drawing is not correct.
     
    Last edited: Sep 17, 2011
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