Really convoluted related rates problem

G

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Whew. I know it has something to do with two triangles.

"A street light is mounted at the top of a 15-foot-tall pole. A man six feet tall walks away from the pole at a speed of 5 ft./sec. along a straight path. How fast is the tip of his shadow moving when he is 40 feet from the pole?"

So you have two things: We know the height of the pole, AND we know the height of the man. The x-value, 40 feet, is going to be the same in both triangles. We know dx/dt = 5 ft./sec. All we need to know is the shadow part...and that's where they lose me.

Any suggestions?
 
Isn't this one of the most famous calculus problems? I had the same problem on an exam of mine awhile back...

Anyway you need to realize that there are two similar triangles. You need to set up a ratio equation with the values given, and then you can cross multiply. Usually when the equation is set up, it will be easier to differentiate implicitly, though its up to you. There is more than one way to do this problem, though.

You will get to a point where you have a dy/dt and a dx/dt. You know dx/dt is 5 ft/sec, but a lot of problems in this "section" if I remember correctly give too much information.
 
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