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Math Help - vectors

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    Question vectors

    An airplane is flying due north at 440 miles per hour. A wind begins to blow in the direction South 45 degrees East (S45E) at 59 miles per hour. Find the bearing the pilot must fly the aircraft to continue traveling due north.

    The correct answer is North 11.8 degrees West or N11.8W. I'm not sure how they got that answer. I'd really appreciate some help...ASAP!!!!!!!!! PLEASE. THANKS!
    Last edited by iheartthemusic29; March 16th 2008 at 04:48 PM.
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  2. #2
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    Quote Originally Posted by iheartthemusic29 View Post
    An airplane is flying due north at 440 miles per hour. A wind begins to blow in the direction South 45 degrees East (S45E) at 59 miles per hour. Find the bearing the pilot must fly the aircraft to continue traveling due north.

    The correct answer is North 11.8 degrees West or N11.8W. I'm not sure how they got that answer. I'd really appreciate some help...ASAP!!!!!!!!! PLEASE. THANKS!
    1. Draw a sketch.

    2. The flight of the airplane is described by \vec a= \left(\begin{array}{c}0\\440 \end{array}\right) and the wind can be described by \vec w= \left(\begin{array}{c}\frac{59}2 \sqrt{2}\\ -\frac{59}2 \sqrt{2} \end{array}\right)

    3. Therefore the course over ground (cog) is \vec c = \vec a + \vec w . That means:

    \vec c = \left(\begin{array}{c}\frac{59}2 \sqrt{2}\\ 440-\frac{59}2 \sqrt{2} \end{array}\right)

    4. To calculate \alpha use the tan-function:

    \tan(\alpha) = \frac{\frac{59}2 \sqrt{2}}{440-\frac{59}2 \sqrt{2}}~\implies~ \alpha \approx 5.9798...^\circ

    5. I've no idea where the given result comes from What I mean: The pilot is steering N, the airplane is flying N5.98E so it must be sufficient if the pilot steers to N5.98W ...?
    Attached Thumbnails Attached Thumbnails vectors-flugzg_gegenwind.gif  
    Last edited by earboth; March 16th 2008 at 10:05 PM.
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