Final answer:
The magnitude of the car's velocity vector, with 25 km/h North and 38 km/h West components, is found using the Pythagorean theorem, yielding approximately 45.49 km/h.
Step-by-step explanation:
To determine the magnitude of the car's velocity vector when the car travels 25 km/h North and 38 km/h West, we must use the Pythagorean theorem because the velocities are at right angles to each other. This situation forms a right-angled triangle with the velocities as the two perpendicular sides.
Let vN = 25 km/h (velocity to the North) and vW = 38 km/h (velocity to the West). The magnitude of the velocity vector v can be found using the following equation:
|°v°| = √(vN² + vW²)
|°v°| = √(25² + 38²) km/h
|°v°| = √(625 + 1444) km/h
|°v°| = √2069 km/h
|°v°| = 45.49 km/h (rounded to 2 decimal places)
The magnitude of the car's velocity vector is therefore approximately 45.49 km/h.