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## Homework Statement

A goose starts in flight a miles due east of its nest. Assume that the goose maintains constant flight speed (relative to the air) so that it is always flying directly toward its nest. The wind is blowing due north at w miles per hour. Figure 8 shows a coordinate frame with the nest at (0,0) and the goose at (x,y). It is easily seen that

[itex]\frac{dx}{dt}[/itex] = -v

_{0}cosθ

[itex]\frac{dy}{dt}[/itex] = w - v

_{0}sinθ

Show that

[itex]\frac{dy}{dx}[/itex] = [itex]\frac{y - k\sqrt{x^{2} + y^{2}}}{x}[/itex]

where k = w/v

_{0}, the ratio of the wind speed to the speed of the goose.

## Homework Equations

See Above

## The Attempt at a Solution

I don't see how the above can be the solution. x' and y' are constant so dx/dy should just be y/x, shouldn't it?