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Math Help - Plane type of question

  1. #1
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    Plane type of question

    Hello, this question is from Grade 12 Calculus and Vectors book.

    A pilot in an airplane with an airspeed of 1000 km/hr wishes to fly to a city 2000km due east. There is a wind blowing from bearing of 025^\circ<br />
at a speed of 100 km/hr. In what heading should the pilot seer

    B) What will be the ground speed of the plane

    C) How long will this trip take
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  2. #2
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    Quote Originally Posted by daunder View Post
    Hello, this question is from Grade 12 Calculus and Vectors book.

    A pilot in an airplane with an airspeed of 1000 km/hr wishes to fly to a city 2000km due east. There is a wind blowing from bearing of 025^\circ<br />
at a speed of 100 km/hr. In what heading should the pilot seer

    B) What will be the ground speed of the plane

    C) How long will this trip take
    wind blowing from a 025^{\circ} bearing is blowing toward -115^{\circ} relative to East.

    let \theta be the airplane's heading relative to East.

    desire the resultant velocity in the y direction (North-South) to be 0 so the plane will track due East ...

    North component of plane's velocity + South component of wind's velocity = 0

    1000\sin{\theta} + 100\sin(-115) = 0

    \sin{\theta} = \frac{\sin(115)}{10}

    \theta \approx 5.2^{\circ}

    groundspeed = 1000\cos(5.2) + 100\cos(-115) \approx 954 km/hr

    t = \frac{2000}{1000\cos(5.2) + 100\cos(-115)} \approx 2.1 hrs
    Last edited by skeeter; April 8th 2009 at 03:35 PM. Reason: fixed groundspeed
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