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A light is hung 15 feet above a straight horizontal path If a man 6 feet tall is walking away from the light at the rate of 5 feet per second how fast is his shadow lenghtening?
Devilish31
Suppose the distance from the light to the man at time t is x(t), and that the length of his shadow is s(t).By similar triangles, (x + s)/s = 15/6 = 5/2
That is, x/s + 1 = 5/2 so that x/s = 3/2
and therefore, s = 2x/3
Then since dx/dt = 5 feet/sec, ds/dt = 2/3*5 ft/sec = 10/3 ft/sec or 3.33... (recurring) ft/sec
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