Related Rates Homework Problem

1. Nov 13, 2006

muna580

I am trying to do the problem below but I don't understand how to do it. Can you please show me how to do it? DON'T give me the answer, explain to me how to get the answer.

http://img134.imageshack.us/img134/9168/untitled1au7.jpg [Broken]

Point C moves at a constant rate along semicircle centered at ) from A to B. The radius of the semicircle is 10 cm, and it takes 30 sec for C to move from A to C. Angle COB has measure y radians, angle OCA has measure z radians, and AC = x cm as indicated in the figure.

a) What is the rate of change, in radians per sec, of x with respect to time?

b) What is the rate of change, in radians per sec, of y with respect to time?

c) x and y are related by the Law of Cosines; that is, y^2 = 10^2 + 10^2 - 2(10)(10)cos y. What is the rate of change of x with respect to time when y = π/2 radians?

d) Let D be the area of ΔOAC. Show that D is largest when x = π/2 radians.

Last edited by a moderator: May 2, 2017
2. Nov 13, 2006

HallsofIvy

Staff Emeritus
The first thing you should do is go back and take the time to copy the problem correctly! You have consistently confused x and y!

You just told us that x is measured in cm, not radians! Do you mean "in cm per sec" or do you mean rate of change of y?

Well, they've pretty much given you the answer right there! Except that, of course you mean x^2= 10^2+ 10^2- 2(10)(10)cos y. Differentiate both sides of that with respect to t. You were also told that "it takes 30 sec for C to move from A to C" which doesn't really make sense. I think you meant that it take 30 sec for the moving point to move from A to C. Unless you are given some information about exactly where C is, I don't see how that helps you! Since they specify y= $\pi$/2 radians, do they mean it take 30 seconds to go from A to $\pi$/2 radians?

The altitude of that triangle is 10 sin(y). (And again, x cannot be "$\pi/2$ radians", it is a length. Presumably, you meant y.)

Last edited by a moderator: May 2, 2017
3. Mar 9, 2011

alyssajune

Can you help me with the problem below except:

angle AOC = x
angle ACO = y
and AC = s
Thanks!!!

4. Mar 9, 2011

Char. Limit

Aside from the fact that you're hijacking a four-year-old thread, you need to show some work before we help you with a problem. It's forum policy.