Final answer:
The statement that a person's total displacement will be the same despite taking a wrong turn and walking in the opposite direction for the second part of their journey is False. Displacement considers both magnitude and direction, which would differ with a wrong turn.
Step-by-step explanation:
The statement is False. Displacement is defined as the vector that points from the initial position to the final position of a movement, regardless of the path taken. The person walked 2 km east, but then walked 1 km south instead of north for the second part of the journey. Therefore, the magnitude of the displacement would differ if the person had followed the directions correctly and walked north instead.
The original question can be analyzed through vector addition. The initial correct displacement would have been a vector with components (2 km east, 1 km north). Taking a wrong turn and walking south instead of north would result in (2 km east, -1 km south). These two vectors have different north-south components and thus, their magnitudes are different.
If we represent the two scenarios graphically, the correct path forms a right-angled triangle with sides 2 km and 1 km, and the displacement can be found using the Pythagorean theorem. On the other hand, the wrong turn still forms a right-angled triangle, but in the opposite direction in the north-south axis, resulting in a different displacement vector.