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Calculus

The pilot of an airplane that flies with an airspeed of 800 km/h wishes to travel to a city 800 km due east. There is a 80 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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music123

  1. A is angle he heads North of East
    plane velocity due to wind in East direction = -80 cos 45
    plane velocity due to heading in East dir = 800 cos A
    total East component = 800 cos A - 80 cos 45

    plane velocity due to wind in North direction = -80 sin 45
    plane velocity due to heading in North dir = 800 sin A

    We want ZERO North resultant so
    800 sin A = 80 sin 45
    sin A = 0.1 (.707) = 0.0707
    A = 4 degrees North of East or 90 - 4 = 86 deg compass heading

    now velocity component East = 800 cos 4 - 80 cos 45
    = 798 - 56.56 = 741 km/hr East
    800 / 741 = hours taken

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