November 11th, 2012, 03:01 PM  #1 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Intimidating ROC problem
ok guys, of all the problems I have done this Semester...it is the nasty Rate of Change Problems that make me the most uncomfortable. Obviously this is an area (amoung so many others ) that I need some serious review help in for the following problems I have looked in textbook as well as notes I have taken and many of my posts on this forum. Sadly to say I have to beg for help still. Here goes... A right triangle has a fixed base of length 6 Meters and a height that is INCREASING at a rate of 2 Meters/Second. At what rate is the length of the HYPOTENUSE increasing when the HEIGHT IS 8 METERS ? Any and all help and guidance will be especially apprieciated on this one 
November 11th, 2012, 03:08 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Intimidating ROC problem
How can you relate the 3 sides of the right triangle?

November 11th, 2012, 03:09 PM  #3 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Re: Intimidating ROC problem
via the Pythagorean Theorem ?

November 11th, 2012, 03:14 PM  #4 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 635 Thanks: 96 Math Focus: Electrical Engineering Applications  Re: Intimidating ROC problem
mathkid, Write an equation for the hypotenuse length in terms of h and the base length, 6. Then take the derivative of the hypotenuse length wrt h. Then use the chain rule to get the derivative of the hypotenuse length wrt time and plug in the values. But the first step is to write an equation for the hypotenuse in terms of h and the base length, 6. Hint: do not use the square root sign. Use a power of 1/2 as it will make taking the derivative easier (for me, anyway). EDIT: Sorry, did not see [color=#00BF00]MarkFL[/color] had answered. Please follow his advice. 
November 11th, 2012, 03:16 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Intimidating ROC problem
Bingo! So write the relation, bear in mind that the base is fixed (constant) and implicitly differentiate with respect to time, solve for the time rate of change of the hypotenuse, then plug in the given values for the time rate of change of the vertical leg and for that of the length of the hypotenuse. edit: One way is to do as [color=#0000FF]jks[/color] has suggested, and another way is to use implicit differentiation, which to me is computationally simpler. 
November 11th, 2012, 03:21 PM  #6 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Re: Intimidating ROC problem
It's still very GREEK to me Mark. I get so frustrated with these RR problem because I don't really have a grasp on the concept. with what u guys said im thinking h^2 = x^2 + y^2 so imp diff with respect to h I think would be like 2h = 2x dx/dh + 2y dy/dh I wish I understood this better instead everytime I see a Related Rate problem I get nervous and frustrated 
November 11th, 2012, 03:29 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Intimidating ROC problem
You want to differentiate with respect to time t: Noting that x is a constant, we find: We are told (in m/s...I would include this in the LaTeX but it gets mangled by LaTeX now) and are asked to find the time rate of change of the hypotenuse when it is in length. Now, the only thing we need is to find when. How can we do this? 
November 11th, 2012, 03:30 PM  #8 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Re: Intimidating ROC problem
mark this is how I feel about these related rate problems Listen to this what this girl says lol http://www.youtube.com/watch?v=Vi5KBiXg0Co 
November 11th, 2012, 03:36 PM  #9 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Re: Intimidating ROC problem
Mark, I try to follow and see this: dh/dt = y/h(2) sorry I again cant seem to grasp it I think I am trying to understand it with arithmatic thinking 
November 11th, 2012, 03:40 PM  #10 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Intimidating ROC problem
What is y when h is 8? Once you find this, then you will have the value for dh/dt in m/s.


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