A man goes 10 m towards North, then 20 m towards east then displacement is

Options

A. 22.5 m
B. 25 m
C. 25.5 m
D. 30 m

Explanation

To solve the problem of finding the displacement of a man who moves 10 m towards the North and then 20 m towards the East, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Movement**:
- The man first moves 10 m North.
- Then, he moves 20 m East.

2. **Visualize the Path**:
- We can represent the movements on a coordinate system.
- Starting from the origin (0,0), after moving North, the new position will be (0, 10) (0 m East, 10 m North).
- After moving East, the final position will be (20, 10) (20 m East, 10 m North).

3. **Determine the Displacement**:
- Displacement is the straight-line distance from the starting point to the final position.
- We can use the Pythagorean theorem to find this distance.
- The displacement can be represented as the hypotenuse of a right triangle where:
- One side (AB) is the distance moved North (10 m).
- The other side (BC) is the distance moved East (20 m).

4. **Apply the Pythagorean Theorem**:
- According to the theorem, the displacement \( AC \) can be calculated as:
\[ AC = \sqrt{AB^2 + BC^2} \]
- Substituting the values:
\[ AC = \sqrt{(10)^2 + (20)^2} \]
\[ AC = \sqrt{100 + 400} \]
\[ AC = \sqrt{500} \]

5. **Simplify the Result**:
- We can simplify \( \sqrt{500} \):
\[ \sqrt{500} = \sqrt{100 \times 5} = 10\sqrt{5} \]
- Approximating \( \sqrt{5} \) (which is approximately 2.236):
\[ AC \approx 10 \times 2.236 = 22.36 \text{ m} \]

6. **Final Answer**:
- The displacement of the man is approximately \( 22.36 \) meters.