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Calculus/calculus-shadow problem

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Expert: - 4/24/2008


Question
ray needay is 6 ft tall and he is walking away from a 24 ft tall lamp post at 4 ft per second. how fast is rays shadow lengthening when his distance from the lamp post is the (square root of 5e)/pie

Answer
This looks like two similar triangles.  Let y be the shadow length and x be the distance from his feet to the pull.  It is know that
y/6 = (x+y)/24.  Solve for y, find dy/dx, and this is how fast the end of the shadow is moving out.

What I just thought about is that this will tell you how fast the end of the shadow is moving out.  To see how fast the shadow is lengthening, don't you also have to take into account that the shadow is getting shorter at his feet at 4ft/sec?  Might want to ask the instructor of this course about that.

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