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A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 7 ft/s along a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole?

  • Math - ,

    make a sketch
    label the man's distance from the post as x
    and the length of his shadow y
    by similar triangles and ratios
    6/y = 15/(x+y)
    15y = 6x + 6y
    9y = 6x
    3y = 2x
    3dy/dt = 2dx/dt
    dy/dt = (2/3)(7) = 14/3 ft/s
    so the length of his shadow is lengthening at 14/3 ft/s
    but it is moving at 14/3 + 7 or 35/7 ft/sec

  • Math - ,

    Thank you very much!

    By the way, 14/3+7 equals 35/3, not 35/7.

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