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Math Help - Find components using only 1 vector and 1 angle

  1. #1
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    Find components using only 1 vector and 1 angle

    Hi, I'm trying to figure out the solution to this question:

    "If a force has magnitude 100 and is directed 45 south of east, what are its components?"

    I diagrammed it so that I have a the vector with magnitude 100 and the vector going south-east at 45, and so far I can only tell that the components of the first vector are <100, 0>. Where do I go from here?

    Thanks for your help.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Find components using only 1 vector and 1 angle

    Quote Originally Posted by bumpjump View Post
    Hi, I'm trying to figure out the solution to this question:

    "If a force has magnitude 100 and is directed 45 south of east, what are its components?"

    I diagrammed it so that I have a the vector with magnitude 100 and the vector going south-east at 45, and so far I can only tell that the components of the first vector are <100, 0>. Where do I go from here?

    Thanks for your help.
    Use trigonometry to find x and y (your components) .
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  3. #3
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    Re: Find components using only 1 vector and 1 angle

    Quote Originally Posted by Also sprach Zarathustra View Post
    Use trigonometry to find x and y (your components) .
    A quick google search says SOHCAHTOA only works for right triangles; this is equilateral since the given angle is 45 degrees. What trig function will give me the components of the unknown vector?
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  4. #4
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    Re: Find components using only 1 vector and 1 angle

    First, an equilateral triangle has angles of 60 degrees, not 45! Second, given any one angle, you can always construct a right triangle having that as one of its angles. Draw x, y coordinates and think of "east" to the right, "north" upward, so "west" to the left, "south" downward. An angle "45 south of east" is at 45 degrees below the positive x-axis (the line to the right). Draw a line at that angle, of length 1. Drop a perpendicular from the end of that line to the x-axis. Now do you see the right triangle?

    " I have a the vector with magnitude 100 and the vector going south-east at 45, and so far I can only tell that the components of the first vector are <100, 0>."

    Are you clear on what "components" of a vector are? There is no vector here that has components <100, 0>. If a vector \vec{v}= a\vec{i}+ b\vec{j}, where \vec{i} and \vec{j} are the unit vectors in the directions of the positive x and y axes ("east" and "north" here) then the components of the vector are <a, b>. The length of that vector is \sqrt{a^2+ b^2}. Neither of the components of this given vector is 100. Its length is 100.
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