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A plane is capable of flying 200 km/h. There is a wind of 90 km/h from the east. The pilot flies in a northwest direction relative to the ground for three hours from city A to city B. Find the speed of the plane relative to the ground, the heading of the plane, and the distance between city A and city B.

  • Physics -

    Cosine Law
    u=sqrt(V²+v²-2•V•v•cos135°)=
    =sqrt(200²+90²-2•200•90•cos135°)=
    =sqrt(40000+8100 +25455.8)=271 km/h
    s=u•t=271•3=813 km
    Sine Law
    271/sin135°=90/sinβ
    sinβ=90•sin135°/271=0.235
    β=13.6° (northwest, respectively west direction)

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