Final answer:
To calculate the total displacement of the cyclist, decompose the distances traveled into their respective north-south and east-west components, sum them, and then convert the resultant vector back into magnitude and direction.
Step-by-step explanation:
The subject of this question involves calculating the total displacement of a cyclist after two segments of a trip. To find the net displacement, we will decompose the individual vectors of each leg of the trip into their north-south and east-west components and then sum these components to get the final displacement vector.
The first leg of the trip is 127m West 28° North (W28N), which can be decomposed into:
- Northward component = 127m * cos(28°)
- Westward component = 127m * sin(28°)
The second leg is 210m South 28° West (S28W), which can also be decomposed into:
- Southward component = 210m * cos(28°)
- Westward component = 210m * sin(28°)
By summing the northward (positive) and southward (negative) components, and doing the same for the westward components, the total displacement can be determined. Remember to transform the resultant vector back into magnitude and direction to give a complete answer.