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Math Help - vertical and horizontal components (forces)

  1. #1
    Senior Member euclid2's Avatar
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    vertical and horizontal components (forces)

    find the horizontal and vertical components of a force of 75N that acts in a direction forming an angle of 51 degrees with the vertical.
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  2. #2
    Member alexgeek's Avatar
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    Just use trig,
    F_v = 75 \cos(51)
    F_h = 75 \sin(51)
    Attached Thumbnails Attached Thumbnails vertical and horizontal components (forces)-temp.jpg  
    Last edited by alexgeek; September 14th 2010 at 07:56 AM. Reason: Added diagram
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  3. #3
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    Hello, euclid2!

    Did you make a sketch?


    Find the horizontal and vertical components of a force of 75N
    that acts in a direction forming an angle of 51 degrees with the vertical.

    In the diagram, "d" represents "degrees".


    Code:
          |           o A
          |         * :
          |    75 *   :
          |     *     :
          |51d        :
          | * 39d     :
        O * - - - - - + - -
          |           B

    In right triangle ABO\!:\;\;O\!A = 75,\;\angle AOB = 39^o

    The horizontal component is OB.
    The vertical component is AB.

    Therefore: . \begin{Bmatrix} \cos39^o \:=\:\dfrac{OB}{75} & \Rightarrow & OB \;=\;75\cos39^o \;\approx\;58.3 \\ \\[-3mm]<br />
\sin39^o \:=\:\dfrac{AB}{75} & \Rightarrow & AB \:=\:75\sin39^o \;\approx\;47.2 \end{Bmatrix}

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