Final answer:
To find the car's total displacement, one must calculate the vector components of the 98 km southwest portion of the trip and add them to the 210 km displacement to the west.
Step-by-step explanation:
The total displacement of a car that is driven 210 km west and then 98 km southwest can be found using vector addition. The displacement to the west is simply 210 km in the westward direction. For the southwest portion, this is a diagonal movement in a grid, so it can be split into two components: one to the south and one to the west. Since the angle given is 45°, the southward and westward components will be equal. To find these components, you can use trigonometric functions, specifically the cosine and sine of 45° (which are both √2/2). Multiplying 98 km by √2/2 gives us the southward and westward displacement components of the second part of the trip. Finally, these components are added vectorially to the initial 210 km displacement to the west. The resulting vector gives us the total displacement from the starting point.
- Calculate the westward component of the 98 km southwest trip.
- Calculate the southward component of the 98 km southwest trip.
- Add the results to the initial 210 km westward displacement.
The magnitude of the total displacement can then be calculated using the Pythagorean theorem if needed.