Solving Problems with Vectors and Velocity Practice Test

Given the velocities, a person walks at $\vec v_{\text{person/train}}=2\ \text{m/s}$ due west relative to a train, while the train moves at $\vec v_{\text{train/ground}}=10\ \text{m/s}$ due east relative to the ground. How fast is the person moving relative to the ground (magnitude and direction)?

For the situation described, an airplane’s velocity relative to the air is $\vec v_{\text{plane}}=300\ \text{km/h}$ due east, and the wind velocity is $\vec v_{\text{wind}}=50\ \text{km/h}$ due south. What is the magnitude of the plane’s ground velocity $|\vec v_{\text{ground}}|$?