A man walk 10 m towards east, then 40 m towards North and in the last 30 m towards west find the net displacement :-

Options

A. 20 m
B. `20 sqrt 5 m`
C. 30 m
D. `30 sqrt 5 m`

Answer

To solve the problem of finding the net displacement of the man who walks in different directions, we can follow these steps:

### Step 1: Understand the Directions
The man walks in three different directions:
1. 10 m towards East
2. 40 m towards North
3. 30 m towards West

### Step 2: Visualize the Movement
Let's visualize the movements on a coordinate plane:
- Starting point (origin) is (0, 0).
- After walking 10 m East, the new position is (10, 0).
- After walking 40 m North, the new position is (10, 40).
- After walking 30 m West, the new position is (10 - 30, 40) = (-20, 40).

### Step 3: Determine the Final Position
The final coordinates of the man after all movements are (-20, 40).

### Step 4: Calculate the Net Displacement
Net displacement is the straight-line distance from the starting point (0, 0) to the final point (-20, 40). We can use the distance formula:
\[ \text{Displacement} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates:
\[ \text{Displacement} = \sqrt{(-20 - 0)^2 + (40 - 0)^2} = \sqrt{(-20)^2 + (40)^2} = \sqrt{400 + 1600} = \sqrt{2000} \]
\[ \text{Displacement} = \sqrt{2000} = \sqrt{100 \times 20} = 10\sqrt{20} \approx 44.72 \text{ m} \]

### Final Answer
The net displacement is approximately **44.72 m**.

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