Chasing a Polar Goose (UMAP)

A goose due east of its nest begins to fly home. It always flies directly toward the nest at constant airspeed b, but a wind from the south at constant speed w blows it off course. How fast must the goose fly to get home? If the wind were blowing in the face of the goose, the goose would need to fly faster than the wind; but does the not-too-clever goose gain an advantage when it need not face the wind head-on?

Table of Contents:

FLIGHT OF THE GOOSE

THE RECTANGULAR GOOSE

THE POLAR GOOSE

A PAIR OF CONJECTURES
From Rectangular to Polar
...And From Polar to Rectangular
Thinking Geometrically

EXTENSIONS

THE RETURN OF THE GOOSE

REFERENCES

ACKNOWLEDGMENT

ABOUT THE AUTHORS