Final answer:
To find the resultant of the two vectors, we resolve the vector at an angle into its components, combine with the purely eastward vector, and then use the Pythagorean theorem and arctangent function to find the magnitude and direction of the resultant.
Step-by-step explanation:
To find the resultant of the two given vectors: 2.00 x 10m due east and 4.00 x 10m 30.0° north of west, we must break down the second vector into its east-west (x-axis) and north-south (y-axis) components.
The eastward vector is straightforward as it only has an eastward component of 2.00 x 10m. For the vector pointing 30.0° north of west, we use trigonometry to resolve it into its components:
- Westward (x-axis): 4.00 x 10m × cos(30.0°)
- Northward (y-axis): 4.00 x 10m × sin(30.0°)
Finally, since the vectors are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the resultant vector R, and the arctangent function to find its direction relative to the east.
Remember to provide the magnitudes of the x and y components and to subtract the westward component from the eastward component since they are in opposite directions.