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Math Help - application 2

  1. #1
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    application 2

    problem: Two posts, one 3 meters high and the other 6 meters high, stand 10 meters apart. They are to be stayed by wires attached to a single stake at ground level, the wires running to the tops of the posts. Where should the stake be placed to use the least amount of wire?
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  2. #2
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    Hello, cazimi!

    This is one of the more unpleasant problems . . .


    Two posts, one 3m high and the other 6m high, stand 10m apart.
    They are to be stayed by wires attached to a single stake at ground level,
    the wires running to the tops of the posts.
    Where should the stake be placed to use the least amount of wire?
    Code:
                                      *C
                                    * |
                                  *   |
                                *     |
         A*                   *       | 6
          |  *              *         |
        3 |     *         *           |
          |        *    *             |
         B* - - - - - * - - - - - - - *D
          :     x     P     10-x      :

    AB is the 3-meter pole; CD is the 6-meter pole.
    They are 10 meters apart: BD = 10.

    The wire runs from A to a point P on the ground, then up to C.
    Let x = BP, then PD = 10 - x.


    From the right triangles (and Pythagorus), we have:
    . . . . . . . . ______ . . . . . . . .___________
    . . AP .= .√x + 3, . CP .= .√(10 - x) + 6


    The length of the wire is: .L .= .[x + 9]^ + [(10 - x) + 36]^

    And that is the function you must minimize.

    I'll wait in the car . . .

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    There is a very clever geometric approach to this problem
    . . which eliminates the need for all that Calculus.
    I'll let someone else explain it.

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