Final answer:
To find the distances you would have to fly straight south and then straight west to arrive at the same point, you can break down the displacement using sine and cosine of the angle. For the given values, the total distance is 31.7 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 can use the same method. For these values, the total distance is 31.9 km.
Step-by-step explanation:
To find the distances you would have to fly straight south and then straight west to arrive at the same point, we can break down the displacement into its components. The displacement in the south direction can be found using sine of the angle and the displacement in the west direction can be found using cosine of the angle. We can then use the Pythagorean theorem to find the total distance.
- Displacement south = 32.0 km * sin(35.0°) = 18.4 km
- Displacement west = 32.0 km * cos(35.0°) = 26.2 km
- Total distance = √(displacement south^2 + displacement west^2) = √(18.4 km^2 + 26.2 km^2) = 31.7 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, we can use the same method:
- Displacement south of west = 32.0 km * sin(45.0°) = 22.6 km
- Displacement west of north = 32.0 km * cos(45.0°) = 22.6 km
- Total distance = √(displacement south of west^2 + displacement west of north^2) = √(22.6 km^2 + 22.6 km^2) = 31.9 km