Answer :
Final answer:
The displacement from Albany after two stages of movement is 597 miles 59.1 degrees North of West. Each stage of the movement is broken down into its directional components and are added up for the final displacement determination.
Explanation:
This problem is about determining the displacement after a series of movements. Displacement is a vector quantity which means that it has both magnitude (distance) and direction.
The first part of the journey is 481 miles at 42.9 degrees north of west. We can break this down into westward and northward components. Westward component = 481 miles * cos(42.9 degrees), Northward component = 481 miles * sin(42.9 degrees).
The second part of the journey is 116 miles at 16.2 degrees north of east. This also can broken down into eastward and northward components. Eastward component = 116 miles * cos(16.2 degrees), Northward component = 116 miles * sin(16.2 degrees).
Finally, we sum up these components for both directions and determine the resultant displacement using Pythagorean theorem. We would also need to use inverse tangent function to determine the resultant angle. An accurate calculation would lead to the choice (d) 597 miles 59.1 degrees North of West.
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