weight on a pulley

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Pookers

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Dec 11, 2005
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Hey guys.

My teacher gave me a writing prompt to do about a problem that we've never had anything close to. Any help would be much appreciated.

A weight is attached to a rope 50 ft long which passes over a pulley at P, 20 ft above the ground. The other end of the rope is attached to a truck at point A, 2 ft above the ground. If the truck moves off at the rate of 9 ft/sec, how fast is the weight rising when it is 6 ft above the ground?

I've can't think of how to start this one. Thanks for any help, even just getting me started.
 
You need some Right Triangles.

For starters, you may wish to drive the truck off a little until the weight is two feet off the ground. That might simplify things a bit. After that, how long is the rope from pulley to truck? The vertical distance, pulley to weight, is 18 ft, right?

If there is a trick on this one, it is probably that the rope is a fixed TOTAL length. The distance from weight to pulley to truck remains constant, 50 ft.
 
So if the truck is moved forward so the weight is 2 ft off the ground you get a right triangle. With this, you can find that if you put it in standard pythagorean triangle form, a=18, b=26.46, and c=32 feet...

Shouldn't I be able to take the derivative of pythagorean theorem, yielding:

2a(da/dt)+2b(db/dt)=2c(dc/dt)

and then if plug in what I know:

2(18)(da/dt)+2(26.46)(9)=2(32)(dc/dt)

Now I'm stuck with 2 variables that I can't figure out how to find. Please help!
 
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