Final answer:
To add the given vectors, first find the x and y components of each vector. Then, add the x-components together and the y-components together. Finally, use the Pythagorean theorem to find the magnitude of the resultant vector.
Step-by-step explanation:
To add the given vectors, we need to break each vector into its x and y components. Let's start with the first vector, which has a magnitude of 2.0 m/s and is 30° north of east. The x-component of this vector can be found using the cosine function: 2.0 m/s * cos(30°) = 1.732 m/s. The y-component can be found using the sine function: 2.0 m/s * sin(30°) = 1.0 m/s. Repeat the same process for the second vector, which has a magnitude of 4.0 m/s and is 75° north of east. The x-component is 4.0 m/s * cos(75°) = 1.045 m/s and the y-component is 4.0 m/s * sin(75°) = 3.858 m/s. Now, add the x-components together: 1.732 m/s + 1.045 m/s = 2.777 m/s. Add the y-components together: 1.0 m/s + 3.858 m/s = 4.858 m/s. Finally, use the Pythagorean theorem to find the magnitude of the resultant vector: sqrt((2.777 m/s)^2 + (4.858 m/s)^2) = 5.651 m/s. Therefore, the magnitude of the resultant vector is approximately 5.651 m/s.