A man has to go 50 m due north, 40 m due east and 20 m due south to reach a field, What distance he has to walk to reach the field? b.What is his displacement from his house to the field?

Explanation

To solve the problem step by step, we need to determine both the total distance traveled by the man and his displacement from his house to the field.

### Step 1: Calculate the Total Distance Traveled
1. The man travels 50 meters due north.
2. He then travels 40 meters due east.
3. Finally, he travels 20 meters due south.

**Total Distance = Distance North + Distance East + Distance South**
\[ \text{Total Distance} = 50 \, \text{m} + 40 \, \text{m} + 20 \, \text{m} = 110 \, \text{m} \]

### Step 2: Calculate the Displacement
Displacement is the shortest straight-line distance from the initial point (his house) to the final point (the field).

1. **Draw a diagram**: Represent the movements on a coordinate system.
- Start at point A (the house).
- Move to point B (50 m north).
- Move to point C (40 m east).
- Move to point D (20 m south).

2. **Identify the coordinates**:
- Point A (0, 0)
- Point B (0, 50)
- Point C (40, 50)
- Point D (40, 30) (since he moves 20 m south from point B)

3. **Calculate the displacement (AD)**:
- The coordinates of point A are (0, 0) and the coordinates of point D are (40, 30).
- Use the Pythagorean theorem to find the distance AD:
\[ AD = \sqrt{(x_D - x_A)^2 + (y_D - y_A)^2} \]
\[ AD = \sqrt{(40 - 0)^2 + (30 - 0)^2} = \sqrt{40^2 + 30^2} \]
\[ AD = \sqrt{1600 + 900} = \sqrt{2500} = 50 \, \text{m} \]

### Final Answers
- **Total Distance Traveled**: 110 meters
- **Displacement**: 50 meters