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Math Help - Vectors and Velocity

  1. #1
    Sky
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    Vectors and Velocity

    A plane heads on a bearing of 210 degrees at 500 mph; the winds at the cruising altitude are 75 mph from the southwest to the northeast.

    Write the vector u representing the velocity of the plane relative to the air and the vector v representing the velocity of the wind.

    Can someone please help and explain this to me?
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  2. #2
    Sky
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    If I worked this out correctly, I think vector u = <-250√3,-250>
    and vector v = <-75,0>.

    Is this right?
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  3. #3
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    Quote Originally Posted by Sky View Post
    A plane heads on a bearing of 210 degrees at 500 mph; the winds at the cruising altitude are 75 mph from the southwest to the northeast.

    Write the vector u representing the velocity of the plane relative to the air and the vector v representing the velocity of the wind.

    Can someone please help and explain this to me?
    this really is not a good venue for teaching ... hopefully you have been taught the basics.

    start by making a sketch ... note that the directions are more than likely referenced to true north.

    Air vector + Wind vector = Ground vector

    you can manipulate vectors using the law of sines/cosines or by using components.
    Attached Thumbnails Attached Thumbnails Vectors and Velocity-airvectors.jpg  
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  4. #4
    Sky
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    Here is my sketch:



    Upon further evalution, this seems to be incorrect. Ugh.
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  5. #5
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    3 digit bearings are usually measured clockwise from true north ... otherwise, the problem usually uses the 30 degrees west of south type of description.
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  6. #6
    Sky
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    Whoops.
    Here we go?

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  7. #7
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    ok ... u and v = ???
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  8. #8
    Sky
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    u = <-250,-250√3>
    v = <-75,0>

    ?

    And the ground vector = <-325,-250√3> ?
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  9. #9
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    vector v (the wind vector) blowing NE at 75 mph ...

    \vec{v} = \left<\dfrac{75\sqrt{2}}{2},\dfrac{75\sqrt{2}}{2}\  right>
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  10. #10
    Sky
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    Ah. Okay.

    So, in turn, the ground vector would equal <-197,-380> ?
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  11. #11
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    Quote Originally Posted by Sky View Post
    Ah. Okay.

    So, in turn, the ground vector would equal <-197,-380> ?
    come on ... you can add components as easily as I can.
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  12. #12
    Sky
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    Quote Originally Posted by skeeter View Post
    come on ... you can add components as easily as I can.
    I'll take that as a yes.
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