To determine the runner's displacement from the origin, we need to understand the concept of displacement in physics. Displacement is defined as the shortest distance from the initial position to the final position, along with the direction. It is a vector quantity, meaning it has both magnitude and direction. ### Step-by-Step Explanation: 1. **Identify the Starting Point**: The runner starts at the origin, which we can denote as point O (0 meters). 2. **First Movement**: The runner runs 300 meters north. - After this movement, the runner's position is now 300 meters north of the origin. We can denote this position as point A (300 meters north). 3. **Second Movement**: The runner then turns around and runs 100 meters south. - To visualize this, we can think of the runner moving back towards the origin. Since the runner was at 300 meters north and runs 100 meters south, we can calculate the new position: - Position after running south = Position at A - Distance run south - Position after running south = 300 meters north - 100 meters south = 200 meters north. 4. **Final Position**: The runner's final position is now 200 meters north of the origin. We can denote this position as point B (200 meters north). 5. **Calculate Displacement**: Now, we need to find the displacement from the origin (point O) to the final position (point B). - Displacement = Final position - Initial position - Displacement = 200 meters north - 0 meters = 200 meters north. ### Conclusion: The runner's displacement from the origin is **200 meters north**. ### Evaluating the Options: - **A. 100 meters north**: This option is incorrect because it does not account for the total distance the runner moved north before turning around. The runner ended up 200 meters north, not 100 meters. - **B. 200 meters north**: This is the correct answer, as we calculated the final position to be 200 meters north of the origin. - **C. 300 meters**: This option is misleading because it does not specify a direction. While the runner did run a total of 300 meters north initially, the displacement is concerned with the final position relative to the starting point, which is 200 meters north. - **D. 400 meters**: This option is incorrect as it suggests a total distance traveled rather than displacement. The runner did not end up 400 meters from the origin; instead, they ended up 200 meters north. ### Summary: - Displacement is the shortest distance from the starting point to the final position, including direction. - The runner's movements were 300 meters north followed by 100 meters south, resulting in a final position of 200 meters north. - The correct answer is **200 meters north** (Option B). - Always remember to consider both distance and direction when calculating displacement.