Go Back   Physics Help Forum > College/University Physics Help > General Physics

General Physics General Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Jun 12th 2010, 07:35 AM   #1
Junior Member
 
Join Date: Apr 2010
Posts: 12
Question regarding rate of change

Sorry if this belongs on the math forum, it's been down all day.

The question:

A 5m ladder is leaning against a vertical wall. Suppose that the bottom of the ladder is being pulled away from the wall at a rate of 1m/s. How fast is the area of the triangle underneath the ladder changing at the instant that the top of the ladder is 4m from the floor?

My attempt:

A = (1/2)xy

dA/dt = dA/dx + dx/dt

dA/dt = (1/2)(dx/dt)y + (1/2)(dy/dt)x

Sub in y = 4, x = 3 (using trig),

dA/dt = 3.5(dy/dt)

I'm not sure if I'm doing this correctly, it doesn't seem right that I'd have to solve for dy/dx. The answer is supposed to be 7/8.

Any assistance would be great!
Glitch is offline   Reply With Quote
Old Jun 14th 2010, 03:09 AM   #2
Member
 
Join Date: Jun 2010
Location: CT, USA
Posts: 35
The chain rule application was incorrect. However, the line after it was fine. But then, I never saw any use of the Pythagorean theorem, which is necessary to relate x and y. There is one step in which you seem to have regarded dx/dt and dy/dt as like terms?!? I would start the problem as follows:

x^2+y^2=25, and hence
x(dx/dt)+y(dy/dt)=0.

Also, A=(xy)/2, and therefore
dA/dt=(x(dy/dt)+y(dx/dt))/2.

You know dx/dt, so by virtue of an equation above, you should be able to figure out dy/dt. Once you have x, dx/dt, y, and dy/dt, you just plug into the expression for the derivative of the area, and you're done. I think you had most of the basic ideas correct, just some mechanics of solving it were incorrect.

Incidentally, what happens as y->0?
__________________
"Tell me and I forget. Show me and I remember. Involve me and I understand." - Confucius
"Excite and direct the self-activities of the pupil, and as a rule tell him nothing that he can learn himself." - The Seven Laws of Teaching, by John Milton Gregory
Ackbeet is offline   Reply With Quote
Old Oct 7th 2010, 11:02 PM   #3
Junior Member
 
Join Date: Oct 2010
Posts: 5
I believe the reason he teaches it like this is because the class is AP Physics B, which is the non-calculus AP Physics. I guess that teaching it this way somehow makes it easier for the students not sure how, but that's just me, given an object thrown into the air at 10 m/s, I would just graph a curve of its displacement and use its equation and derivatives thereof to find its position/velocity/acceleration at any given time point.

Last edited by werehk; Oct 8th 2010 at 01:34 AM.
Will John is offline   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > General Physics

Tags
change, question, rate



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
rate of hydrogen change into helium ling233 Nuclear and Particle Physics 1 Oct 19th 2014 06:24 PM
Mass flow rate question Padawan Thermodynamics and Fluid Mechanics 0 Oct 17th 2011 07:44 PM
A Question about Density, Rate of Flow and Momentum alexgeek Kinematics and Dynamics 2 Jan 20th 2011 02:40 PM
rate harimakenji Kinematics and Dynamics 2 Aug 9th 2010 01:51 AM
Very quick question change in momentum brentwoodbc Energy and Work 3 May 29th 2009 10:01 PM


Facebook Twitter Google+ RSS Feed