A person moves `30 m` north,`, then `20 m towards east and finally `30sqrt(2) m` in south-west direction. The displacement of the person from the origin will be

Options

A. 10 m along North
B. 10 m long South
C. 10 m along West
D. Zero

Explanation

To find the displacement of the person from the origin after moving in the specified directions, we can break down the movements into vector components and then sum them up.

### Step-by-Step Solution:

1. **Define the Movements**:
- The person moves 30 m north.
- Then, 20 m east.
- Finally, 30√2 m in the southwest direction.

2. **Convert Movements into Vector Form**:
- The movement north can be represented as:
\[ \vec{OA} = 0 \hat{i} + 30 \hat{j} \]
- The movement east can be represented as:
\[ \vec{AB} = 20 \hat{i} + 0 \hat{j} \]
- The movement in the southwest direction means moving at a 45-degree angle towards the south-west. The components can be calculated as:
\[ \vec{BC} = -30\sqrt{2} \cos(45^\circ) \hat{i} - 30\sqrt{2} \sin(45^\circ) \hat{j} \]
Since \(\cos(45^\circ) = \sin(45^\circ) = \frac{1}{\sqrt{2}}\), we can simplify:
\[ \vec{BC} = -30\sqrt{2} \cdot \frac{1}{\sqrt{2}} \hat{i} - 30\sqrt{2} \cdot \frac{1}{\sqrt{2}} \hat{j} = -30 \hat{i} - 30 \hat{j} \]

3. **Sum the Vectors**:
- Now, we can find the total displacement vector \(\vec{OC}\) by adding all the vectors:
\[ \vec{OC} = \vec{OA} + \vec{AB} + \vec{BC} \]
Substituting the values:
\[ \vec{OC} = (0 \hat{i} + 30 \hat{j}) + (20 \hat{i} + 0 \hat{j}) + (-30 \hat{i} - 30 \hat{j}) \]
Simplifying this gives:
\[ \vec{OC} = (0 + 20 - 30) \hat{i} + (30 + 0 - 30) \hat{j} = -10 \hat{i} + 0 \hat{j} \]

4. **Interpret the Result**:
- The displacement vector \(\vec{OC} = -10 \hat{i} + 0 \hat{j}\) indicates that the person is 10 m in the negative x-direction (west) from the origin.

### Final Answer:
The displacement of the person from the origin is **10 m towards the west**.