If in aeroplane is moving on a circular path with a uniform speed 300 km /h, then the change in velocity after quarter of the circle will be

Options

A. `150 km//h`
B. zero
C. `600 km//h`
D. `300sqrt2 km //h`

Explanation

To solve the problem of finding the change in velocity of an airplane moving in a circular path after covering a quarter of the circle, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Information:**
- The speed of the airplane, \( v = 300 \, \text{km/h} \).
- The angle covered after a quarter of the circle, which is \( \theta = 90^\circ \).

2. **Understanding Change in Velocity:**
- The change in velocity (\( \Delta v \)) can be calculated using the formula:
\[ \Delta v = 2v \sin\left(\frac{\theta}{2}\right) \]

3. **Substituting the Values:**
- Since \( \theta = 90^\circ \), we can substitute this into the formula:
\[ \Delta v = 2 \times 300 \times \sin\left(\frac{90^\circ}{2}\right) \]
- This simplifies to:
\[ \Delta v = 2 \times 300 \times \sin(45^\circ) \]

4. **Calculating \( \sin(45^\circ) \):**
- We know that \( \sin(45^\circ) = \frac{1}{\sqrt{2}} \).
- Therefore, substituting this value gives:
\[ \Delta v = 2 \times 300 \times \frac{1}{\sqrt{2}} \]

5. **Simplifying the Expression:**
- This can be simplified further:
\[ \Delta v = \frac{600}{\sqrt{2}} = 300\sqrt{2} \, \text{km/h} \]

6. **Final Answer:**
- The change in velocity after the airplane covers a quarter of the circle is:
\[ \Delta v = 300\sqrt{2} \, \text{km/h} \]