A trough filled w/ water's 2m long & has a cross section in the form of an isosceles trapezoid 30 cm wide at the bottom, 60 cm at the top & a height of 50 cm. If the trough leaks water at the rate of 2000 cm^3 / min, how fast is the water level falling when the water is 20 cm. deep.?

Question

A trough filled w/ water's 2m long & has a cross section in the form of  an isosceles trapezoid 30 cm wide at the bottom, 60 cm at the top & a height of 50 cm. If the trough leaks water at the rate of 2000 cm^3 / min, how fast is the  water level falling when the water is 20 cm. deep.?

anonymous · Answer

@mukushla

datanewb · Answer

Hey there, not sure how far along you are in solving this problem, but the first step is to get an equation which relates the volume to the height. Once you have done that, rates of change usually involve differentiation. Since there are two rates of change, for volume and height, this problem lends itself well to implicit differentiation. Here is a very good video on implicit differentiation: http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/lecture-5-implicit-differentiation/

datanewb · Answer

I figured enough time had passed, so here is the answer I got with the full work.  Could someone check it?  I'm learning this too, and not 100% confident.  Thanks.

anonymous · Answer

@datanewb the link you've given is not found..:(

datanewb · Answer

I'm sorry the link is not working for you. I tested it in IE and Chrome and it is working on my computer. As an alternative to the above link, you can go to http://ocw.mit.edu and navigate to mathematics -> 18.01 -> lectures -> lecture 5. Or, simply do a Google search for "18.01 lec 5". The lecture video is the first result returned by Google. It's a 45 minute lecture, and the explanation builds off of the chain rule, so you should be familiar with that before watching the video. (The chain rule is explained in lecture 4).

anonymous · Answer

@datanewb  someone like you here at openstudy...gave me that answer too....however, he told me that the given V' is negative 2000 cm^3/min. for the problem stated above that its leaking a volume of 2000 right? so his answer is -5/2 cm/min..
which is which?? thank you!!

datanewb · Answer

Well, yes, it would be negative.  Generally speaking you can set the isosceles trapezoid in any reference frame, and thus the answer could be negative or positive depending on how you framed the answer.  The only thing that is imperative is that you be consistent.

That said, as I drew the figure and framed my answer, the correct answer is certainly negative. -5/21 cm/s!

Thank you for pointing out my error!

amistre64 · Answer

the negative in this case represents a direction as opposed to a decrease of speed.  thats understood right?

anonymous · Answer

yes...thank you!!