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Math Help - one more vector problem

  1. #1
    Junior Member
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    one more vector problem

    The quiz is as under:

    two forces whose magnitudes are in the ratio 3:7 give a resultant of 3 sq.root of 79 N. If the angle of inclination be 60 degrees, find the magnitude of each force.

    F1 be 3x and F2 be 7x. Resultant F is sq.root of 79. Since the inclination is 60 degree, I take the angle as 30 degrees. One side of the triangle is 3x, second one is 7x and third one is 3 sq.root 79 and one of the angles of the triangle is 30 degrees.

    Whether my assumptions are correct and if so, how to go about?

    Kindly guide me.

    Thanks in advance.
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  2. #2
    Super Member

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    Re: one more vector problem

    Hello, arangu1508!

    \text{Two forces whose magnitudes are in the ratio }3:7\text{ give a resultant of }3\sqrt{79}\text{ N.}
    \text{If the angle of inclination is }60^o\text{, find the magnitude of each force.}

    F_1 = 3x,\;F_2 = 7x,\;\text{ resultant }F = 3\sqrt{79}.
    \text{Since the inclination is }60^o\text{, I take the angle as }30^o.
    \text{One side of the triangle is }3x\text{, second is }7x\text{, and third is }3\sqrt{79}
    \text{And one of the angles of the triangle is }30^o. . No!

    You assumed that the diagonals of a parallelogram bisect the vertex angles.
    . . This is not true . . .

    We have this parallelogram:
    Code:
                        7x
                *  *  *  *  *  *  *
               *                 *
              *                 *
          3x *                 * 3x
            *                 *
           * 60          120 *
          *  *  *  *  *  *  *
                  7x
    which gives us this triangle:
    Code:
                                  *
                              *  *
                   __     *     *
                 3√79 *        * 3x
                  *           *
              *          120 *
          *  *  *  *  *  *  *
                   7x
    Now we can use the Law of Cosines:
    . . \big(3\sqrt{79}\big)^2 \:=\:(3x)^2 + (7x)^2 - 2(3x)(7x)\cos120^o

    Got it?

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  3. #3
    Junior Member
    Joined
    Aug 2011
    Posts
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    Re: one more vector problem

    Mr. Soroban,

    Thank you. I got it.

    with regards,

    Aranga
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