Final answer:
To determine the plane's total distance and direction of the path from its starting point after changing directions, we must use vector addition to combine the two displacement vectors graphically. The resultant vector's magnitude and direction give the total displacement and its angle, which need to be calculated with the components of the initial vectors. The effect of wind from the north would alter the path, depending on wind speed and the plane's airspeed.
Step-by-step explanation:
The student's question pertains to the use of a graphical method to find the total distance a plane covers from the starting point and the direction of the path to the final position, after flying 40.0 km at 60° north of east and then 30.0 km at 15° north of east. To solve this, we need to add the two displacement vectors graphically.
- First, draw the first vector 40.0 km long at a 60° angle north of east.
- Then, from the end of this vector, draw the second vector 30.0 km long at a 15° angle north of east.
- The resultant vector from the starting point to the end of the second vector is the total displacement.
To find the magnitude, use the Pythagorean theorem on the components of the vectors. To find the direction, use the arctangent function on the ratio of the northward to eastward components. This calculation would show that neither of the distances provided in the options (70.0 km or 50.0 km) are correct, because the vectors must be combined by adding their components, not their magnitudes. The direction would also be different from the straightforward addition of angles. The correct answer should be calculated based on the actual component values. Moreover, if there were a wind from the north, it would affect the flight by pushing the plane southwards. The effect of this wind would depend on both the wind speed and the relative airspeed of the plane. A stronger wind or a slower plane would result in a greater deviation from the intended path.