A man moves towards 3m north then 4 m towards east and finally 5 m towards `37^(@)` south of west. His displacement from origin is :-

Options

A. `5sqrt(2)m`
B. 0m
C. 1m
D. 12m

Answer

To find the displacement of the man from the origin after moving in the specified directions, we can break down his movements into components and then calculate the resultant displacement vector.

### Step-by-Step Solution:

1. **Initial Movements:**
- The man first moves **3 m North**. This can be represented as:
\[ \text{Position after 1st movement} = (0, 3) \]
- Next, he moves **4 m East**. This can be represented as:
\[ \text{Position after 2nd movement} = (4, 3) \]

2. **Final Movement:**
- The man then moves **5 m at 37° South of West**. To find the components of this movement, we need to break it into its x (East-West) and y (North-South) components.
- The angle South of West means we need to consider the negative y-direction for the south component and the negative x-direction for the west component.
- The x-component (West) is:
\[ x = -5 \cos(37^\circ) \]
- The y-component (South) is:
\[ y = -5 \sin(37^\circ) \]

3. **Calculating the Components:**
- Using the values of cosine and sine for 37°:
\[ \cos(37^\circ) \approx 0.8 \quad \text{and} \quad \sin(37^\circ) \approx 0.6 \]
- Therefore, the components become:
\[ x = -5 \times 0.8 = -4 \quad \text{(West)} \]
\[ y = -5 \times 0.6 = -3 \quad \text{(South)} \]

4. **Final Position Calculation:**
- Adding these components to the previous position (4, 3):
- For the x-coordinate:
\[ x_{\text{final}} = 4 + (-4) = 0 \]
- For the y-coordinate:
\[ y_{\text{final}} = 3 + (-3) = 0 \]
- Thus, the final position of the man is:
\[ (0, 0) \]

5. **Displacement Calculation:**
- The displacement from the origin (0, 0) is simply:
\[ \text{Displacement} = \sqrt{(0 - 0)^2 + (0 - 0)^2} = 0 \]

### Final Answer:
The displacement from the origin is **0 m**.