How Does Observer Motion Affect Detected Fish Concentration Changes?

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Homework Help Overview

The problem involves understanding how the concentration of fish in a lake, described by the function c(x,y) = 1/(x² + y²), changes as observed by a moving observer in a boat versus a stationary observer. The observer is traveling away from a feeding point at a speed of 10 m/s.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formulation of the concentration function and consider the implications of the observer's motion. There is a suggestion to express the concentration in terms of polar coordinates and to calculate the rate of change with respect to distance from the feeding point.

Discussion Status

Some participants have offered insights on changing coordinate systems and applying the chain rule to relate the changes observed by the moving observer to those of a stationary observer. However, the discussion does not indicate a consensus or resolution of the problem.

Contextual Notes

The original poster expresses difficulty in starting the problem, indicating a potential gap in understanding the application of the concepts involved. There is also a mention of a solution being reached, but the details of that solution are not provided.

banerjeerupak
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Homework Statement



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.

Homework Equations





The Attempt at a Solution



Can someone give me how to start solving this problem. I'm having trouble making a start at it.
 
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I'm guessing that the concentration of fish is actually
[tex]c(x, y)~=~\frac{1}{x^2 + y^2}[/tex]

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?
 
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
 
Thank you very much... question solved.
 

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