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Calculus- rates

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A man 6ft. tall walks at the rate of 5 ft/sec toward a streelight that is 16 ft. above the ground. At what rate is the length of his shadow changing when he is 10ft. from the base of the light?

  • Calculus- rates -

    x is shadow tip from streetlight
    y is man from streetlight
    from similar triangles
    x/16 = (x-y)/6
    16 x - 16 y = 6 x
    16 y = 10 x
    x = 1.6 y
    dx/dt = 1.6 dy/dt
    = 1.6*5

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