An aeroplane is flying with a uniform speed of 300 km/h along a circular path. The change in velocity after half the circular track is covered, is given by

Options

A. `300 sqrt(2)` km/h
B. 600 km/h
C. `600 sqrt(2)` km/h
D. 300 km/h

Explanation

To find the change in velocity of an aeroplane flying along a circular path after covering half of the circular track, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial and Final Velocities**:
- The aeroplane starts at point A and moves along a circular path. At point A, the velocity (V) is directed tangentially to the circle in a specific direction.

2. **Determine the Direction of Velocity at Halfway Point**:
- After covering half of the circular path, the aeroplane reaches point B. At this point, the direction of velocity will be directly opposite to that at point A. Therefore, the final velocity (V') at point B is equal in magnitude but opposite in direction to the initial velocity.

3. **Express the Initial and Final Velocities**:
- Initial velocity (V) at point A = 300 km/h (in a certain direction).
- Final velocity (V') at point B = -300 km/h (in the opposite direction).

4. **Calculate the Change in Velocity**:
- The change in velocity (ΔV) is given by the formula:
\[ \Delta V = V' - V \]
- Substituting the values:
\[ \Delta V = (-300 \text{ km/h}) - (300 \text{ km/h}) = -600 \text{ km/h} \]

5. **Magnitude of Change in Velocity**:
- The magnitude of the change in velocity is:
\[ |\Delta V| = 600 \text{ km/h} \]

### Final Answer:
The change in velocity after half the circular track is covered is **600 km/h**.

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