Final answer:
The northern and western displacements of the hurricane are approximately 385 km north and 558 km west, respectively, which is calculated using trigonometric functions cosine and sine for the north of west direction of travel.
Step-by-step explanation:
The student is asking to find the northern and western displacement of a hurricane that travels 678 km at 34.60 degrees north of west before turning into a tropical storm. To solve this, we can decompose the overall displacement into its northern and western components using trigonometric functions.
Given the hurricane's path makes an angle of 34.60 degrees north of west, we can calculate the westward (x-component) and northward (y-component) displacements by using the cosine and sine functions, respectively:
- Western displacement (x-component) = Total displacement × cos(angle)
- Northern displacement (y-component) = Total displacement × sin(angle)
Calculations:
- x-component = 678 km × cos(34.60°) = 558 km (approximately)
- y-component = 678 km × sin(34.60°) = 385 km (approximately)
Thus, the correct answer is 558 km west and 385 km north, which corresponds to option (a).