March 29, 2017

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A 6ft tall woman is walking away from a srteet lamp at 4 ft/sec that is 24ft tall. How fast is the length of her shadow changing?

  • calculus - ,

    It depends upon her distance from the swtreet lamp at the time. Did they not tell you that distance?

  • calculus - ,

    no time given

  • calculus - ,

    Make a sketch. Draw a line from the top of the street lamp to the end of her shadow
    I see two similar right-angled triangles.
    Let the length of her shadow be x ft
    let her distance to the street lamp be y

    then 24/(x+y) = 6/x
    which simplifies to
    3x = y
    3dx/dt = dy/dt
    dx/dt = 4/3 ft/s

    In this type of question, the length of her shadow is growing at a uniform rate, independent of the time passed or her position.
    Secondly, had the question been, "how fast is her shadow moving?" you would have to add her speed to the 4/3.

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