Final answer:
The magnitude and direction of the resultant vector are determined by adding the x and y components of the two vectors using trigonometry and then applying the Pythagorean theorem and inverse tangent function.
Step-by-step explanation:
To find the magnitude and direction of the sum of two coplanar displacement vectors, one at 20m at 0° and the other at 10m at 120°, you can use the component method. First, break each vector into its horizontal (x-axis) and vertical (y-axis) components. For the first vector (20m at 0°), this will result in components of 20m (x) and 0m (y).
For the second vector (10m at 120°), the components can be found using trigonometry: 10m*cos(120°) for the x-component and 10m*sin(120°) for the y-component.
After calculating the components for each vector, add the corresponding components to find the resultant vector's components. Then, use the Pythagorean theorem to determine the magnitude of the resultant vector, and the arctangent function (tan⁻¹ or atan) to find its direction. The direction should be expressed with respect to the positive x-axis (0° line).