What is the total distance and displacement of a person who walks 3m east, 2 m north, 1m west, and then 2 m south?

To calculate the total distance and the displacement of the person, we can break down their movements. 1. **Total Distance**: The total distance is simply the sum of all the distances traveled regardless of direction. - 3 m east - 2 m north - 1 m west - 2 m south Total distance = 3 m + 2 m + 1 m + 2 m = 8 m 2. **Displacement**: Displacement is the straight-line distance from the starting point to the ending point, taking direction into account. We can calculate the resultant position based on the movements. Let's denote the movements on a coordinate grid: - Starting at the origin (0, 0): - Move 3 m east: (3, 0) - Move 2 m north: (3, 2) - Move 1 m west: (2, 2) - Move 2 m south: (2, 0) The final position is (2, 0). Now, we will calculate the displacement, which is the straight-line distance from the starting point (0, 0) to the ending point (2, 0). Using the distance formula: \[ \text{Displacement} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] where \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (2, 0)\). Substituting the coordinates: \[ \text{Displacement} = \sqrt{(2 - 0)^2 + (0 - 0)^2} = \sqrt{2^2} = \sqrt{4} = 2 \text{ m} \] In conclusion: - Total distance walked = **8 m** - Displacement = **2 m**