A person moves 30 m north. Then 30 m east, then `30sqrt(2)` m south-west. His displacement from the original position is

Options

A. zero
B. 28 m towards south
C. 10 m towards west
D. 15 m towards east

Explanation

To find the displacement of the person from the original position after moving in the specified directions, we can break down the movements step by step and use vector addition.

### Step-by-Step Solution:

1. **Movement North**:
- The person moves 30 m north.
- This can be represented as a vector: \( \vec{A} = (0, 30) \) where the first component is the east-west direction (x-axis) and the second component is the north-south direction (y-axis).

2. **Movement East**:
- Next, the person moves 30 m east.
- This can be represented as a vector: \( \vec{B} = (30, 0) \).

3. **Movement South-West**:
- Finally, the person moves \( 30\sqrt{2} \) m in the south-west direction.
- The south-west direction can be broken down into equal components in the south and west directions. Since the angle is 45 degrees, the components can be calculated as:
- South component: \( \frac{30\sqrt{2}}{\sqrt{2}} = 30 \)
- West component: \( \frac{30\sqrt{2}}{\sqrt{2}} = 30 \)
- Thus, this movement can be represented as a vector: \( \vec{C} = (-30, -30) \).

4. **Total Displacement Calculation**:
- Now, we can find the total displacement vector \( \vec{D} \) by adding the three vectors:
\[ \vec{D} = \vec{A} + \vec{B} + \vec{C} = (0, 30) + (30, 0) + (-30, -30) \]
- Performing the addition:
\[ \vec{D} = (0 + 30 - 30, 30 + 0 - 30) = (0, 0) \]

5. **Magnitude of Displacement**:
- The magnitude of the displacement is given by the formula:
\[ |\vec{D}| = \sqrt{(0)^2 + (0)^2} = 0 \]

### Conclusion:
The displacement of the person from the original position is **0 m**.