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A street light is at the top of a 19 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 feet from the base of the pole?

  • Calculus - ,

    Let her distance from the pole be x ft
    let the length of her shadow by y ft

    given: dx/dt = 7 ft/s
    find: d(x+y)/dt when x = 30

    by ratios:
    19/(x+y) =6/y
    19y = 6x+6y
    13y = 6x
    13dy/dt = 6dx/dt
    dy/dt = 6(7)/13 = 42/13 ft/s

    (notice dy/dt is a constant , which means the shadow is lengthening and moving at a rate independent of where she is)

    d(x+y)/dt = 7 + 42/13 = 133/13 or appr 10.23 ft/s

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