Well, I'm sorry to bother you all with this exercise, but I can't seem to find the solution.

First of all: no, this is NOT a homework, it's just an exercise in our book, and I'm curious as to what the solution is. I've been trying to find it for over an hour straight, and I just can't figure it out.


A man starts to walk in point P and walks around a circular lake (radius: 3.2 km) with a constant speed of 4.8 km/hour. The position of the man is R.
How fast does the length of the cord PR change, when PÔR = 60°?

Oh, and we saw this exercise with Derivatives, just mentioning ;-)
Anyone care to try?

Can you post a link to a diagram of this problem, if possible?

Or you could tell us where Ô is. The angle PÔR is meaningless if you don't define Ô. If Ô is the centre of the lake the length of the cord PR changes at 4.8*sin60=4.157km/hour when PÔR = 60°

Oh, oops.
Yes, Ô is the centre of the lake.
Sorry!
Could you explain your answer too?

Explaining the answer would either involve a bunch of formulas (if you want calculus and derivatives used in the explanation) or a bunch of drawings (if you want an explanation using vector analysis), both of which are most easily provided by sitting at a desk with you.

Maybe you can make our lives a little easier by explaining what you are trying to do and how far you've got?

Thanks!

Groetjes,

Kees-Jan

Well, I'm trying to calculate it using calculus and derivatives.
I'm sorry for bothering you all with this, and I feel rather stupid asking this question (normally, I don't have any problems calculating derivatives).

Here's a picture:
http://img.photobucket.com/albums/v1...ol/picture.jpg

Well, then. The length of a can be found using the cosine rule (using the angle POR). POR itself is a function of radus r, velocity v and time t.

You can then compute the derivative of a using the chain rule (twice, I think).

Where exactly do you get stuck?

Groetjes,

Kees-Jan

PS. You are pushing "general" to its limit, aren't you :-)

Silly me! I didn't think about the cosine rule ops:
I understand it now :-)
Thanks!

PS. Yes, I know :-P