# Calculating rate of change

1. Dec 4, 2009

### banerjeerupak

1. The problem statement, all variables and given/known data

The concentration c of fish away from a feeding point in a lake is given by c(x,y) = 1/(x2 + y2). Find the total change of fish concentration detected by an observer riding a boat traveling with a speed u = 10 m/s straight away from the feeding point. What is the corresponding change detected by a stationary observer.

2. Relevant equations

3. The attempt at a solution

Can someone give me how to start solving this problem. I'm having trouble making a start at it.

2. Dec 4, 2009

### Staff: Mentor

I'm guessing that the concentration of fish is actually
$$c(x, y)~=~\frac{1}{x^2 + y^2}$$

Since the boat with the observers is moving in a straight line away from the feeding point, c(x, y) = c(r) = 1/r2. Can you calculate the rate of change of concentration with respect to r?

3. Dec 5, 2009

### HallsofIvy

Staff Emeritus
Mark44's idea, to change to "polar coordinates" is excellent. To change from "an observer riding a boat traveling with a speed u = 10" to "a stationary observer", use the chain rule: dc/dt= dc/du du/dt

4. Dec 5, 2009

### banerjeerupak

Thank you very much.... question solved.