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Math Help - Vector basics

  1. #1
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    Vector basics

    Hi I'm new to vectors and I really do not understand how one part came about.

    An airplane needs to fly due east from one city to another at a speed of 400 kmh¡1. However, a 50 kmh¡1 wind blows constantly from the north-east.
    In what direction must the aeroplane head to compensate for the wind, and how does the wind affect its speed?

    Adapted from: IB HL Mathematics Haese and Harris Publications.


    I understand everything about the question like the vector part and all I am just wondering how to get the angle. To calculate the speed the airplane should travel at so as to not be disrupted by the wind vector, the textbook says to use the cosine rule to find out. I understand why but when substituting the values into the cosine rule equation, there is a 135 degrees, which corresponds to the vector which the airplane should ideally travel at to avoid the wind. How did the 135 degrees come about? Can someone help me? Where in the question can I deduce 135 degrees and if there are any steps, could you please list them out? I really need to understand this to continue doing the other questions..

    Thank you so so so much.







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  2. #2
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    Re: Vector basics

    Using the standard that N is located in the direction of the positive y-axis, and angles are measured starting from the positive x-axis, a wind from the NE would make an angle of 90+45 = 135 with the airplane's desired heading, E.

    Vector basics-image.jpg.
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  3. #3
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    Re: Vector basics

    Hi thanks! But how do you know that the wind from NE will displace the plane by an angle of 45 degrees?
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  4. #4
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    Re: Vector basics

    Actually, I wouldn't say that the wind displaces the plane by 45 degrees. The required direction the plane needs to fly needs to be calculated. This is the first question in your post.

    Remember the plane needs to fly slightly into the wind at an angle shown in the picture below as, A. You can find this angle using the law of sines, Sin(A)/50=Sin(135)/400. You will still need to calculate the resulting speed of the airplane to complete the problem.

    Vector basics-image.jpg
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  5. #5
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    Re: Vector basics

    Thank you!
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