To determine the total distance traveled and the displacement of the boy, we can break down the movements step by step.
Total Distance Covered:
- South: 10 km
- East: 5 km
- North: 22 km
Total distance = Distance south + Distance east + Distance north
Total distance = 10 km + 5 km + 22 km = 37 km
Displacement:
Displacement is the shortest straight-line distance from the starting point to the final position, although the boy's path is not a straight line.
-
Final North-South Position:
- Moved south: 10 km
- Moved north: 22 km
- Net movement in the north-south direction: 22 km (north) - 10 km (south) = 12 km (north)
-
East-West Position:
- Moved east: 5 km
Now, we can use the Pythagorean theorem to calculate the displacement:
\[ \text{Displacement} = \sqrt{(\text{North-South Position})^2 + (\text{East-West Position})^2} \] \[ \text{Displacement} = \sqrt{(12 \text{ km})^2 + (5 \text{ km})^2} \] \[ \text{Displacement} = \sqrt{144 + 25} \] \[ \text{Displacement} = \sqrt{169} \] \[ \text{Displacement} = 13 \text{ km} \]
Summary:
- Total Distance Covered: 37 km
- Displacement: 13 km