Final answer:
The pilot's total displacement from the starting point is determined by vector addition and the effects of northern wind on the flight path are counteracted by adjusting the plane's heading appropriately.
Step-by-step explanation:
The question involves analyzing a vector addition problem in physics, where a pilot flies two separate legs on different headings and the task is to find the resultant displacement vector from the starting point. We use the principles of vector addition to compute this total displacement, which is the vector sum of the individual displacements. In the presence of wind, the plane's course must be corrected to achieve the desired heading. This correction angle and the effective ground speed of the plane can be determined by constructing a vector diagram that accounts for the velocity of the plane with respect to the air and the velocity of the air with respect to the ground.
When encountering wind from the north, the pilot must adjust the plane's heading eastward to compensate for the wind pushing the aircraft toward the west. The necessary compensation depends on the relative magnitudes of the wind speed and the plane's airspeed; stronger winds or slower plane speeds would require greater adjustments in the plane's heading. Using the vector diagram, one can calculate the magnitude and direction of the plane's velocity with respect to the ground, and this informs the pilot on the correct course to maintain to reach the desired destination despite wind interference.