Final answer:
The displacement of a person who walks 10 m west, 10 m north, 20 m east, and 20 m south is approximately 14.14 meters, in a direction southeast from the original position.
Step-by-step explanation:
The question asks for the displacement of a person who moves along a certain path. To calculate displacement, which is a vector quantity, one must consider the magnitude and direction from the initial position to the final position regardless of the path taken.
Following the given movements, we can determine the person's overall displacement. The movements were: 10 m west, then 10 m north, then 20 m east, and finally 20 m south. The east-west movement cancels out because 10 m west and 20 m east result in a net displacement of 10 m east. The north-south movement also cancels out because the person moves 10 m north and then 20 m south, resulting in a net displacement of 10 m south.
Therefore, the final displacement of the person is a vector that is 10 m east and 10 m south of the original position. If we want to express this as a single vector, we can apply Pythagorean theorem to find its magnitude:
R = √(x^2 + y^2)
R = √(10^2 + 10^2)
R = √(200)
R = 14.14 m (approximately)
The direction of this displacement vector can be found using trigonometry, specifically by finding the angle with respect to the east or south direction.