Question

a boy sets out to buy food at night starting from his house he moved 10km due south, 5km due east and 22km due north consecutively. Find his total distance and displacement covered

Answer 1

To determine the total distance traveled and the displacement of the boy, we can break down the movements step by step.

### Total Distance Covered:
1. **South:** 10 km
2. **East:** 5 km
3. **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.

1. **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)

2. **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