A person travels towards north by 4 m and then turns to west and travels by 3 m. The distance and displacement are

Options

A. 7 m and 5 m
B. 7 m and 7 m
C. 7 m and 1 m
D. 7 m and 3.5 m

Explanation

To solve the problem of calculating the distance and displacement of a person who travels 4 meters north and then 3 meters west, we can follow these steps:

### Step-by-step Solution:

1. **Understanding the Movement**:
- The person first travels 4 meters to the north.
- Then, the person turns to the west and travels 3 meters.

2. **Calculating the Total Distance**:
- Distance is a scalar quantity that represents the total path length traveled.
- Here, the total distance traveled is the sum of the two segments:
\[ \text{Total Distance} = \text{Distance North} + \text{Distance West} = 4 \, \text{m} + 3 \, \text{m} = 7 \, \text{m}. \]

3. **Calculating the Displacement**:
- Displacement is a vector quantity that represents the shortest straight-line distance from the initial position to the final position.
- To find the displacement, we can use the Pythagorean theorem since the movements form a right triangle:
- The northward movement (4 m) is one leg of the triangle.
- The westward movement (3 m) is the other leg of the triangle.
- According to the Pythagorean theorem:
\[ \text{Displacement} = \sqrt{(\text{North Distance})^2 + (\text{West Distance})^2} = \sqrt{(4 \, \text{m})^2 + (3 \, \text{m})^2}. \]
- Calculating:
\[ \text{Displacement} = \sqrt{16 + 9} = \sqrt{25} = 5 \, \text{m}. \]

4. **Final Results**:
- The total distance traveled is **7 meters**.
- The displacement is **5 meters**.

### Summary:
- **Distance**: 7 meters
- **Displacement**: 5 meters