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

Options

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

Answer

To find the displacement of a man who travels 10 meters north and then 20 meters east, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Movement**:
The man first moves 10 meters in the north direction and then 20 meters in the east direction.

2. **Visualize the Path**:
We can visualize this movement on a coordinate system where:
- The starting point is at the origin (0, 0).
- After moving 10 meters north, the position becomes (0, 10).
- After moving 20 meters east, the final position becomes (20, 10).

3. **Determine the Displacement**:
Displacement is defined as the straight-line distance from the initial position to the final position. We can calculate this using the Pythagorean theorem.

4. **Apply the Pythagorean Theorem**:
The displacement \(d\) can be calculated as:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (20, 10)\).

5. **Substitute the Values**:
\[ d = \sqrt{(20 - 0)^2 + (10 - 0)^2} \]
\[ d = \sqrt{20^2 + 10^2} \]
\[ d = \sqrt{400 + 100} \]
\[ d = \sqrt{500} \]

6. **Calculate the Result**:
\[ d = \sqrt{500} = \sqrt{100 \times 5} = 10\sqrt{5} \]
Approximating \(\sqrt{5} \approx 2.236\):
\[ d \approx 10 \times 2.236 = 22.36 \text{ meters} \]

### Final Answer:
The displacement of the man is approximately **22.36 meters**.

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