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 solve the problem of finding the displacement of a person who moves in three different directions, we can break down the movements step by step.

### Step 1: Understand the Movements
1. The person moves **30 m North**.
2. Then, the person moves **30 m East**.
3. Finally, the person moves **30√2 m South-West**.

### Step 2: Visualize the Movements
- Start at the origin point (0,0).
- Moving **30 m North** takes the person to the point (0, 30).
- Moving **30 m East** takes the person to the point (30, 30).
- Moving **30√2 m South-West** means moving at a 45-degree angle towards the South-West.

### Step 3: Calculate the South-West Movement
The South-West direction can be broken down into its components:
- The South-West movement can be resolved into two equal components (South and West) since it forms a 45-degree angle.
- Each component will be:
\[ \text{Component} = \frac{30\sqrt{2}}{\sqrt{2}} = 30 \text{ m} \]
- Therefore, the person moves **30 m South** and **30 m West**.

### Step 4: Determine the Final Position
- Starting from (30, 30):
- After moving **30 m South**, the new position is (30, 30 - 30) = (30, 0).
- After moving **30 m West**, the new position is (30 - 30, 0) = (0, 0).

### Step 5: Calculate Displacement
- The final position (0, 0) is the same as the original position (0, 0).
- Therefore, the displacement from the original position is:
\[ \text{Displacement} = \sqrt{(0 - 0)^2 + (0 - 0)^2} = 0 \text{ m} \]

### Final Answer
The displacement from the original position is **0 m**.

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