Final answer:
The plane traveled approximately 338.9 miles south and 338.9 miles west.
Step-by-step explanation:
To find the distances the plane has traveled south and west, we need to find the components of the displacement along the south and west directions using trigonometry.
In this case, the plane flies on a bearing of S 489 W for 478 miles. This means it is traveling in the southwest direction.
To find the south and west distances, we can use the sine and cosine functions:
South Distance = 478 miles * sine(45°) = 478 miles * 0.7071 ≈ 338.9 miles
West Distance = 478 miles * cosine(45°) = 478 miles * 0.7071 ≈ 338.9 miles