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 solve the problem of finding the man's displacement from the origin after moving in specified directions, we can break down the movements into components and use vector addition.

### Step-by-Step Solution:

1. **Identify the Movements:**
- The man moves 3 m North.
- Then he moves 4 m East.
- Finally, he moves 5 m at an angle of 37° South of West.

2. **Convert the Last Movement into Components:**
- The last movement can be resolved into its x (East-West) and y (North-South) components.
- The angle South of West means we will have:
- West component (x-direction): \(5 \cos(37^\circ)\)
- South component (y-direction): \(5 \sin(37^\circ)\)

Using the cosine and sine values:
- \( \cos(37^\circ) \approx 0.798\)
- \( \sin(37^\circ) \approx 0.601\)

Therefore:
- West component = \(5 \times 0.798 \approx 3.99 \, \text{m}\) (to the West)
- South component = \(5 \times 0.601 \approx 3.005 \, \text{m}\) (to the South)

3. **Determine the Overall Position:**
- After moving North 3 m, East 4 m, and then 3.99 m West and 3.005 m South, we can calculate the final position:
- **Final x-coordinate (East-West):**
\[ x = 4 \, \text{m (East)} - 3.99 \, \text{m (West)} \approx 0.01 \, \text{m (East)} \]
- **Final y-coordinate (North-South):**
\[ y = 3 \, \text{m (North)} - 3.005 \, \text{m (South)} \approx -0.005 \, \text{m (South)} \]

4. **Calculate the Displacement:**
- The displacement can be calculated using the Pythagorean theorem:
\[ \text{Displacement} = \sqrt{x^2 + y^2} = \sqrt{(0.01)^2 + (-0.005)^2} = \sqrt{0.0001 + 0.000025} = \sqrt{0.000125} \approx 0.0112 \, \text{m} \]

5. **Direction of Displacement:**
- The angle can be calculated using:
\[ \theta = \tan^{-1}\left(\frac{y}{x}\right) = \tan^{-1}\left(\frac{-0.005}{0.01}\right) \approx -26.57^\circ \]
This indicates the direction is slightly South of East.

### Final Answer:
The man's displacement from the origin is approximately **0.0112 m** at an angle of **26.57° South of East**.