A spy report about a suspected car reads as follows. The car moved 2.00 km towards east, made a perpendicular left turn, ran for 500 m, made a perpendicular right turn, ran for 4.00 km and stopped. Find the displacement of the car.

Explanation

To find the displacement of the car based on the given movements, we can break down the problem step by step.

### Step-by-Step Solution:

1. **Understanding the Movements**:
- The car first moves 2.00 km towards the east.
- Then, it makes a left turn and moves 500 m (0.5 km) north.
- Finally, it makes a right turn and moves 4.00 km towards the east again.

2. **Setting Up the Coordinate System**:
- Let's set the starting point (origin) at point O (0,0).
- The positive x-axis will represent the east direction, and the positive y-axis will represent the north direction.

3. **Calculating the Position After Each Movement**:
- **First Movement (East)**:
- From O (0,0) to A (2.00 km, 0) → A(2, 0).
- **Second Movement (North)**:
- From A (2, 0) to B (2, 0.5) → B(2, 0.5).
- **Third Movement (East)**:
- From B (2, 0.5) to C (6, 0.5) → C(6, 0.5).

4. **Finding the Displacement**:
- The displacement vector from the origin O(0, 0) to the final point C(6, 0.5) can be represented as OC.
- The displacement vector OC = C - O = (6 - 0, 0.5 - 0) = (6, 0.5).

5. **Calculating the Magnitude of the Displacement**:
- The magnitude of the displacement vector OC can be calculated using the Pythagorean theorem:
\[ |OC| = \sqrt{(6)^2 + (0.5)^2} = \sqrt{36 + 0.25} = \sqrt{36.25} \]
- Calculating further:
\[ |OC| = \sqrt{36.25} \approx 6.02 \text{ km} \]

### Final Answer:
The displacement of the car is approximately **6.02 km**.