Final answer:
The total distance the person walked is 500.0 m, which is the sum of all the distances walked in each direction. Their displacement, which is the straight-line distance from the start to the end point, is calculated using the Pythagorean theorem and is 360.6 m.
Step-by-step explanation:
The total distance traveled by a person can be found by simply adding up the lengths of each segment of their walk. Since the person walks 100.0 m east, 200.0 m north, and then 200.0 m east again, we just need to sum these distances:
- 100.0 m east + 200.0 m north + 200.0 m east = 500.0 m
Therefore, the total distance traveled is 500.0 m.
However, the displacement is the straight-line distance from the start point to the end point of the walk. The displacement can be found by considering a right-angled triangle, where the base is the total distance traveled east (100.0 m + 200.0 m = 300.0 m) and the height is the total distance traveled north (200.0 m). Using the Pythagorean theorem (a² + b² = c²), we find that the displacement (c) is:
√(300.0 m)² + (200.0 m)² = √(90000 + 40000) m² = √130000 m² = 360.6 m
Thus, the person's displacement is 360.6 m.