A boy moves 400 m towards north, 300 m towards west and again 400 m towards south. Calculate the displacement of the boy from the initial position.

Explanation

To solve the problem of finding the displacement of the boy from his initial position, we can follow these steps:

### Step 1: Understand the Movement
The boy moves in three segments:
1. 400 m North
2. 300 m West
3. 400 m South

### Step 2: Visualize the Path
We can visualize the boy's movements on a coordinate plane:
- Starting point (initial position) is at the origin (0, 0).
- Moving 400 m North takes him to (0, 400).
- Moving 300 m West takes him to (-300, 400).
- Moving 400 m South takes him to (-300, 0).

### Step 3: Determine Final Position
After all movements, the boy's final position is (-300, 0).

### Step 4: Calculate Displacement
Displacement is defined as the shortest distance from the initial position to the final position. We can calculate the displacement using the distance formula:

\[ \text{Displacement} = \sqrt{(x_f - x_i)^2 + (y_f - y_i)^2} \]

Where:
- \( (x_i, y_i) \) is the initial position (0, 0)
- \( (x_f, y_f) \) is the final position (-300, 0)

Substituting the values:

\[ \text{Displacement} = \sqrt{(-300 - 0)^2 + (0 - 0)^2} \]
\[ = \sqrt{(-300)^2} \]
\[ = \sqrt{90000} \]
\[ = 300 \text{ m} \]

### Step 5: Direction of Displacement
The direction of the displacement is towards the west since the final position is at (-300, 0).

### Final Answer
The displacement of the boy from his initial position is **300 m towards the west**.

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