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Math Help - Resultant vectors

  1. #1
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    Resultant vectors

    An airplane is travelling S70W with a resultant ground speed of 414 km/h. The nose of the plane is pointing west with an airspeed of 425 km/h. Determine is the speed and direction of the wind.

    how to solve it?
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  2. #2
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    Quote Originally Posted by kkaa View Post
    An airplane is travelling S70W with a resultant ground speed of 414 km/h. The nose of the plane is pointing west with an airspeed of 425 km/h. Determine is the speed and direction of the wind.

    how to solve it?
    hi

    you will need a diagram to solve this , take a look at the one i attached .

    using the cosine rule ,

    |V_w|^2=425^2+414^2-2(425)(414)\cos 20

    |V_w|=146.09 km/h

    As for the direction , solve for \alpha first

    sine rule ,

    \frac{146.09}{\sin 20}=\frac{414}{\sin \alpha}

    \alpha=75.75^o

    \theta=90-75.75=14.25

    so the direction is S 14.25 E
    Attached Thumbnails Attached Thumbnails Resultant vectors-vectors-diagramsss.jpg  
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  3. #3
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    how did you know the direction of wind supposes tobe
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