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Math Help - Finding a plane's heading and length of trip

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    Finding a plane's heading and length of trip

    The pilot of an airplane that flies at 650 km/h wishes to travel to a city 1000 km due east. There is a 75 km/h wind from the northeast.

    a)What should the plane's heading be?

    b) How long will the trip take?
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  2. #2
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    Quote Originally Posted by RyGuy View Post
    The pilot of an airplane that flies at 650 km/h wishes to travel to a city 1000 km due east. There is a 75 km/h wind from the northeast.

    a)What should the plane's heading be?

    b) How long will the trip take?
    I take it that you've made a sketch of the Air + Wind = Ground velocity vectors ...

    let G = groundspeed along a track due east.

    \theta = heading angle relative to east

    using components ...

    650\cos{\theta} - 75\cos(45) = G

    650\sin{\theta} - 75\sin(45) = 0

    from the second equation ...

    \theta = \arcsin\left[\frac{75\sin(45)}{650}\right] \approx 4.7^\circ

    plane should steer about 5^\circ north of east.

    G \approx 595 km/hr


    ... this problem can also be completed using the law of cosines.
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