Final answer:
To find the total distance and direction of the pilot's flight, vector addition is used. The effect of a northern wind depends on the wind speed and the plane's airspeed, requiring heading adjustments to maintain the correct flight path.
Step-by-step explanation:
The student's question involves finding the resultant vector when a pilot flies two different legs on a flight path and then understanding how wind could affect this flight. To solve this, we can use vector addition, with each leg of the flight represented as a vector.
The first leg of the flight is 40.0 km at 60° north of east, which can be represented as a vector with a certain magnitude in the easterly and northerly direction. The second leg is 30.0 km at 15° north of east. The total distance R from the starting point and the direction of the straight-line path to the final position can be found by adding these two vectors using trigonometry or graphical methods.
Regarding the effect of wind from the north, the flight path would be altered depending on the wind speed and the speed of the plane relative to the air mass. A stronger wind would push the plane further south, while a faster plane speed would minimize this effect. The pilot would need to adjust the heading to compensate for the wind to maintain the intended flight path.