Final answer:
To arrive at the same point, you would have to fly 18.02 km due south and 26.05 km due west. If you first fly 22.63 km in a direction 45.0° south of west and then 22.63 km in a direction 45.0° west of north, you would also arrive at the same point.
Step-by-step explanation:
To find the distances you would have to fly due south and then due west to arrive at the same point, you need to analyze the components of the displacement along the south and west directions. The displacement south can be found using the sine function: displacement south = distance * sin(angle). Therefore, the distance you would have to fly due south is 32.0 km * sin(35.0°) = 18.02 km. Similarly, the displacement west can be found using the cosine function: displacement west = distance * cos(angle). Therefore, the distance you would have to fly due west is 32.0 km * cos(35.0°) = 26.05 km.
To find the distances you would have to fly first in a direction 45.0° south of west and then in a direction 45.0° west of north, you need to analyze the components of the displacement along the south-west and west-north directions. The south-west displacement can be found using the sine function: south-west displacement = distance * sin(angle). Therefore, the distance you would have to fly in a direction 45.0° south of west is 32.0 km * sin(45.0°) = 22.63 km. Similarly, the west-north displacement can also be found using the sine function: west-north displacement = distance * sin(angle). Therefore, the distance you would have to fly in a direction 45.0° west of north is 32.0 km * sin(45.0°) = 22.63 km.