What is the wind velocity in km/h and what angle it it north of east?

  1. A light plane is headed due south with a speed relative to still air of 200 km/h. After 1 hour, the pilot notices that they have covered only 190 km and their direction is not south but southeast. What is the wind velocity in km/h and what angle it it north of east?
     
  2. jcsd
  3. Tide

    Tide 3,137
    Science Advisor
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    The velocity of the wind is the difference between the actual velocity of the plane and the "intended" velocity of the plane.
     
  4. ...

    not really...in the book the intended is 240 km/h but the actual is 180 km and the answer they give is 170 k/h with an angle of 41.5 N of E.
     
  5. Tide

    Tide 3,137
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    Remember, velocity is a vector!
     
  6. but there's no angles given.
     
  7. Tide

    Tide 3,137
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    Due south and southeast sound like angles to me! :-)
     
  8. i still dont get it. :confused: angle is 45 degrees?
     
  9. Tide

    Tide 3,137
    Science Advisor
    Homework Helper

    LaTex doesn't seem to be working so I'll try this:

    The actual speed of the plane is 190/sqrt(2) km/h so it's actual velocity is (1, -1)*190/sqrt(2).

    The "intended velocity of the plane is (0, -1)*200 km/h.

    The difference between them is the wind velocity:
    (190/sqrt(2), 200 - 190/sqrt(2))

    Now just divide the y component by the x component to find the tangent of the angle you're looking for.

    A drawing might help you see it better.
     
  10. HallsofIvy

    HallsofIvy 40,769
    Staff Emeritus
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    That should be the first thing you do!
     
  11. Tide, Does Latex work now? I still don't get the answers that the book got using what you did...
     
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