Complete the following problem. 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 towards it's nest. The wind is blowing due north at a constant speed of w miles per hour. Let (x, y) denote the position of the goose in the coordinate frame shown. (x, y) a 1. Use the following diagram to verify that = = -Vocos (0) and = = w - Vo sin(0). w Wind Goose's Flight Direction VO Cos VO YO sing Diagram Part 2 Diagram Part 1 2. Show that dy _ -kvx2+y? dx xX where k = w/Vo, the ratio of the wind speed to the speed of the goose. (Hint: Note that - dy/dt dx dx/dt and show = = -k sec(0) + tan (0) and use the triangle given above to express the trigonometric functions in terms of x and y.)