math

a light is hung 15 feet above a straight horizontal path. If a man is 6 feet tall is walking away from the light at a rate of 5 feet/sec.
a) how fast is his shadow lengthening?
b) at what rate is the tip of the man's shadow moving?

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  1. Let
    x = distance from light
    s = length of shadow
    Then
    (x+s)/15 = s/6
    s = 2/3 x
    (a) ds/dt = 2/3 dx/dt = 2/3 * 5 = 10/3 ft/s
    (b) 5 + 10/3 = 25/3 ft/s

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    oobleck

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