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 1: Analyze the movements of the car
1. The car moves **2.00 km east**.
2. It makes a **perpendicular left turn** and moves **500 m (0.5 km)** north.
3. It then makes a **perpendicular right turn** and moves **4.00 km east**.

### Step 2: Determine the total movements in the x and y directions
- **East (x-direction)**:
- First movement: 2.00 km (east)
- Third movement: 4.00 km (east)
- Total in x-direction = 2.00 km + 4.00 km = **6.00 km east**

- **North (y-direction)**:
- Second movement: 0.5 km (north)
- Total in y-direction = **0.5 km north**

### Step 3: Calculate the resultant displacement
The displacement can be calculated using the Pythagorean theorem, as the movements in the x and y directions form a right triangle.

\[ \text{Displacement} (d) = \sqrt{(sx)^2 + (sy)^2} \]

Where:
- \( sx = 6.00 \, \text{km} \) (total displacement in the x-direction)
- \( sy = 0.5 \, \text{km} \) (total displacement in the y-direction)

Substituting the values:

\[ d = \sqrt{(6.00)^2 + (0.5)^2} \]

Calculating the squares:

\[ d = \sqrt{36 + 0.25} = \sqrt{36.25} \]

Calculating the square root:

\[ d \approx 6.02 \, \text{km} \]

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