Final answer:
The student's question involves determining the wind's velocity affecting an airplane's motion, which can be calculated using vector operations and trigonometry.
Step-by-step explanation:
The student's question concerns the calculation of the wind velocity affecting an airplane's motion relative to the ground. To determine the velocity of the wind, one can use vector addition or subtraction because the airplane's velocity and the wind's velocity combine to give the resultant velocity of the airplane over the ground. Vector components can be broken down into their respective horizontal and vertical components, which are typically labeled as x and y in a coordinate system. Calculating these requires the use of trigonometric functions such as sine, cosine, and tangent, in conjunction with the given angles.
The directional angle relative to due south can be found using trigonometry once the components of the different velocities are known. Utilizing information such as the plane's heading, wind's effect, and trigonometric identities, one can solve for the wind's magnitude and direction. These calculations are an application of the principles of physics, specifically, kinematics and vector operations.