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Math Help - related rates help:

  1. #1
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    related rates help:

    A baseball diamond is 90ft on a side. (It is really a square). A man runs from first base to second base at 25 ft/sec. At what rate is his distance from the third base decreasing when he is 30ft from the first base?

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  2. #2
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    Hello, ^_^Engineer_Adam^_^!

    A baseball diamond is 90ft on a side.
    A man runs from first base to second base at 25 ft/sec.
    At what rate is his distance from the third base decreasing when he is 30ft from the first base?
    Of course, you made a sketch . . .
    Code:
                        B
                        * 
                      *   * x
                    *       *  A
               90 *           o 
                *       o       *
              *   o    y          *
          C o                       *
              *                   *
                *               *
                  *           *
                    *       *
                      *   *
                        *

    The man is at A.
    His distance from second base is: .x = AB
    . . That distance is decreasing at 25 ft/sec: .dx/dt = -25

    His distance from third base is: .y = AC
    . . We want dy/dt

    From right triangle ABC, we have: .y .= .x + 90

    Differentiate with respect to time: .2y(dy/dt) .= .2x(dx/dt)

    . . and we have: .dy/dt .= .(x/y)(dx/dt) .[1]


    When he is 30 feet from first base, x = 60
    . . And: .y .= .60 + 90 . . y = 30√13
    And we know that: .dx/dt = -25
    . . . . . . . . . . . . . . . . . . . . . . . . . . .__
    Substitute into [1]: .dy/dt .= .60/(30√13) (-25) . .-13.9 ft.sec

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