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Math Help - relative velocity

  1. #1
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    relative velocity

    a plane is seen to travel in a direction [S30 degreesW]. 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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    Quote Originally Posted by checkmarks View Post
    a plane is seen to travel in a direction [S30 degreesW]. 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?
    Let denote the vector \overrightarrow{OW} the plane's velocity and direction through the air, the vector \overrightarrow{OP} the plane's velocity and course over ground and \overrightarrow{OS} the velocity and direction of the wind.

    Then |\overrightarrow{OW} | = |\overrightarrow{PS}|

    Use Cosine rule to calculate the length of \overline{PS}

    I've got |\overrightarrow{OW} |= |\overrightarrow{PS} | \approx 185.897\ \frac{km}{h}
    Attached Thumbnails Attached Thumbnails relative velocity-flugzeug_mitwind.gif  
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