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A street light is mounted at the top of a 6-meter-tall pole. A man 2 m tall walks away from the pole with a speed of 1.4 m/s along a straight path. How fast is the tip of his shadow moving when he is 16 m from the pole?

  • calculus - ,

    same question ....

    just change the necessary numbers

  • calculus - ,

    since you have a calculus class, you probably ought to do it Reiny's way, but sometimes a little simplification can save you some work:

    If the man is x away from pole, ad his shadow length is s, then using similar triangles,

    s/2 = (x+s)/6
    s = 1/2 x
    so, ds/dt = 1/2 dx/dt

    since the tip of the shadow is x+s from the pole, it is moving at

    dx/dt + ds/dt = dx/dt + 1/2 dx/dt = 3/2 dx/dt = 3/2(1.4) = 2.1 m/s

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