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Vector Plane, Calculating Windspeed Question?

  1. Feb 13, 2013 #1
    1. The problem statement, all variables and given/known data
    A plane initially flies south at a velocity of 480 km/h. Aided by a wind, the groundspeed is 528 kmh at 15 degrees east of south.

    Calculate the windspeed and the direction of it






    3. The attempt at a solution

    I got the magnitude of 139.9 km/h but for the angle I Don't know if the angle is down below the horizontal or above the horizontal.
     
  2. jcsd
  3. Feb 13, 2013 #2

    haruspex

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    I don't know which way you're measuring the angle. Pls post your working.
     
  4. Feb 13, 2013 #3
    Yes, Like this

    Untitled2_zps2b530c29.png
     
  5. Feb 13, 2013 #4

    haruspex

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    ok, that's a diagram, but somehow you calculated a speed. Presumably you created an unknown for an angle (which angle?) and wrote down some equations. pls share.
     
  6. Feb 13, 2013 #5
    Ok I did cos law: Wind = √ (528)^2 + (480)^2 - 2(528)(480)cos15 = 139.9
     
  7. Feb 13, 2013 #6

    haruspex

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    Ok, so pick an angle in the diagram that you want to compute and write down an equation involving it and known distances.
     
  8. Feb 13, 2013 #7
    I used the sine law: sintheta/528 = sin15/139.9 = 77.53 degrees.... So the picture where the wind goes up?
     
  9. Feb 14, 2013 #8

    haruspex

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    Ok, so you are measuring the wind angle as E of N, and you get 77.5 degrees. Seems reasonable.
     
  10. Feb 14, 2013 #9

    ehild

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    Well, the longest side of the vector triangle is 528 m, so the greatest angle has to be opposite to it. If one angle is 15° and the other is 77.5°, the third angle is 87.5°: the greatest angle in the triangle, and it is opposite to the side of middle length. So choose 180-77.5 as the angle of the wind.

    ehild
     
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