An aeroplane moving in a circular path with a speed `250 km//h`. The change in velocity in half of the revolution is.

Options

A. `500km//h`
B. `250km//h`
C. `120km//h`
D. zero

Explanation

To find the change in velocity of an aeroplane moving in a circular path after half a revolution, we can follow these steps:

### Step 1: Understand the Initial and Final Velocity
- The aeroplane is moving in a circular path with a constant speed of 250 km/h.
- At the start of the half revolution (let's denote this point as point A), the velocity vector can be represented as \( \vec{V_1} = 250 \, \text{km/h} \, \hat{i} \) (assuming it is moving to the right along the x-axis).

### Step 2: Determine the Final Velocity
- After half a revolution (point B), the aeroplane will be at the opposite side of the circular path. The direction of the velocity vector will now be opposite to the initial direction.
- Thus, the final velocity vector can be represented as \( \vec{V_2} = -250 \, \text{km/h} \, \hat{i} \).

### Step 3: Calculate the Change in Velocity
- The change in velocity \( \Delta \vec{V} \) is given by the formula:
\[ \Delta \vec{V} = \vec{V_2} - \vec{V_1} \]
- Substituting the values:
\[ \Delta \vec{V} = (-250 \, \hat{i}) - (250 \, \hat{i}) = -250 \, \hat{i} - 250 \, \hat{i} = -500 \, \hat{i} \, \text{km/h} \]

### Step 4: Interpret the Result
- The magnitude of the change in velocity is \( 500 \, \text{km/h} \) in the direction opposite to the initial velocity.

### Final Answer
- The change in velocity in half of the revolution is \( 500 \, \text{km/h} \).

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