A man covered following displacements. Find the net displacement of the person
(i) 25m west
(ii)` 20 m 30^(@)` east of south
(iii)`5sqrt(3)m` south
(iv) 10 m east
(v) `10 m 60^(@)` north of west

Answer

To find the net displacement of the person after covering the given displacements, we can break down each movement into its components along the x (east-west) and y (north-south) axes.

### Step-by-Step Solution:

1. **Define the Directions**:
- East is positive x-direction.
- West is negative x-direction.
- North is positive y-direction.
- South is negative y-direction.

2. **List the Displacements**:
- (i) 25 m West
- (ii) 20 m at 30° East of South
- (iii) 5√3 m South
- (iv) 10 m East
- (v) 10 m at 60° North of West

3. **Convert Each Displacement to Components**:
- **Displacement (i)**:
- \( D_1 = -25 \hat{i} + 0 \hat{j} \) (25 m West)
- **Displacement (ii)**:
- \( D_2 = 20 \cos(30°) \hat{i} - 20 \sin(30°) \hat{j} \)
- \( D_2 = 20 \left(\frac{\sqrt{3}}{2}\right) \hat{i} - 20 \left(\frac{1}{2}\right) \hat{j} \)
- \( D_2 = 10\sqrt{3} \hat{i} - 10 \hat{j} \)
- **Displacement (iii)**:
- \( D_3 = 0 \hat{i} - 5\sqrt{3} \hat{j} \) (5√3 m South)
- **Displacement (iv)**:
- \( D_4 = 10 \hat{i} + 0 \hat{j} \) (10 m East)
- **Displacement (v)**:
- \( D_5 = -10 \cos(60°) \hat{i} + 10 \sin(60°) \hat{j} \)
- \( D_5 = -10 \left(\frac{1}{2}\right) \hat{i} + 10 \left(\frac{\sqrt{3}}{2}\right) \hat{j} \)
- \( D_5 = -5 \hat{i} + 5\sqrt{3} \hat{j} \)

4. **Sum the Components**:
- **Total x-component**:
\[ x_{total} = -25 + 10\sqrt{3} + 10 - 5 = -15 + 10\sqrt{3} \]
- **Total y-component**:
\[ y_{total} = -10 - 5\sqrt{3} + 5\sqrt{3} = -10 \]

5. **Calculate the Magnitude of the Net Displacement**:
- The net displacement \( D \) can be calculated using the Pythagorean theorem:
\[ D = \sqrt{(x_{total})^2 + (y_{total})^2} \]
\[ D = \sqrt{(-15 + 10\sqrt{3})^2 + (-10)^2} \]
\[ D = \sqrt{(15 - 10\sqrt{3})^2 + 100} \]
\[ D = \sqrt{(225 - 300\sqrt{3} + 300) + 100} \]
\[ D = \sqrt{625 - 300\sqrt{3}} \]

6. **Final Calculation**:
- This expression can be simplified further if needed, but for practical purposes, we can evaluate it numerically to find the approximate value of the net displacement.

### Final Answer:
The net displacement of the person is approximately **20 meters**.