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Math Help - relative velocity (physics question)

  1. #1
    Junior Member
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    relative velocity (physics question)

    please help!!

    A plane is seen to travel in a direction [S 30 degrees W]. if its ground velocity was 300 km/h and the wind speed is 150 km/h south, what is the plane's velocity relative to the air?
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  2. #2
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    Hello,

    I can give you a hint:

    The plane is flying 300km/h 30deg west of south. It's vertical component (in the southern direction) of its ground velocity is thus 300cos(30).

    Let me know if you are still struggling.
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  3. #3
    Senior Member JaneBennet's Avatar
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    You have \mathbf{v}_{\textrm{ground}}=-300\sin{30^\circ}\mathbf{i}-300\cos{30^\circ}\mathbf{j}=-150(\mathbf{i}+\sqrt{3}\mathbf{j}).

    The wind velocity is \mathbf{w}=-150\mathbf{j}.

    Now use the equation \mathbf{v}_{\textrm{air}}+\mathbf{w}=\mathbf{v}_{\  textrm{ground}} and solve for \mathbf{v}_{\textrm{air}}.
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