Understanding the Movement
The person moves through a series of defined movements. Let's break down each segment to calculate the total displacement.
Movement Breakdown
- 30m North: The person starts by moving 30 meters directly north.
- 20m East: From there, they move 20 meters to the east.
- 20√2 m South-West: Finally, the person moves 20√2 meters in the southwest direction. This movement can be resolved into two components (south and west).
Calculating the Displacement
1. Components of the South-West Movement:
- The south component = 20√2 * (1/sqrt(2)) = 20m
- The west component = 20√2 * (1/sqrt(2)) = 20m
2. Net Movement in Each Direction:
- North-South Direction:
- Total North = 30m
- Total South = 20m
- Net North = 30m - 20m = 10m North
- East-West Direction:
- Total East = 20m
- Total West = 20m
- Net East = 20m - 20m = 0m
Calculating Total Displacement
Using the net movements:
- Overall Displacement: The total displacement can be calculated by considering the net movements. Since there is no east-west movement, the displacement is simply the net north movement.
- Final Displacement: The total displacement is 10m North.
Conclusion
In conclusion, the person’s total displacement after all movements is 10 meters North from the starting point. This simple vector addition illustrates how to compute displacement effectively.