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A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?

  • calculus -

    Let the woman be b feet from the pole, and let her shadow be a feet long.

    Using similar triangles,

    a/6 = (a+b)/16
    so a = 3/5 b

    da/dt = 3/5 db/dt = 3/5 * 4 = 12/5 ft/sec, a constant speed.

    That seems odd. I expected her shadow's length to accelerate, but I don't see an error. These problems usually involve a steadily changing angle, and with the tangent function things speed up quickly. Not so here...

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