A scooter going due east at `10 ms^(-1)` turns right through an angle of `90^(@)`. If the speed of the scooter remain unchanged in taking turn, the change is the velocity the scooter is

Options

A. `20.0 ms^(-1)` south-east direction
B. Zero
C. `10.0ms^(-1)` in south direction
D. `14.14 ms^(-1)` in south-west direction

Explanation

To solve the problem of finding the change in velocity of a scooter that turns right through an angle of 90 degrees while maintaining a constant speed of 10 m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial Velocity:**
- The scooter is initially moving due east with a velocity of \( V_1 = 10 \, \text{m/s} \) in the east direction.

2. **Determine Final Velocity:**
- After turning right through an angle of \( 90^\circ \), the scooter will be moving due south with the same speed. Thus, the final velocity is \( V_2 = 10 \, \text{m/s} \) in the south direction.

3. **Represent Velocities as Vectors:**
- We can represent the initial and final velocities as vectors:
- \( V_1 = 10 \, \text{m/s} \, \hat{i} \) (east direction)
- \( V_2 = 10 \, \text{m/s} \, (-\hat{j}) \) (south direction)

4. **Calculate Change in Velocity:**
- The change in velocity \( \Delta V \) is given by:
\[ \Delta V = V_2 - V_1 \]
- Substituting the vectors:
\[ \Delta V = (0 \, \hat{i} - 10 \, \hat{j}) - (10 \, \hat{i} + 0 \, \hat{j}) = -10 \, \hat{i} - 10 \, \hat{j} \]

5. **Magnitude of Change in Velocity:**
- To find the magnitude of the change in velocity, we use the Pythagorean theorem:
\[ |\Delta V| = \sqrt{(-10)^2 + (-10)^2} = \sqrt{100 + 100} = \sqrt{200} = 10\sqrt{2} \, \text{m/s} \]
- This simplifies to approximately \( 14.14 \, \text{m/s} \).

6. **Direction of Change in Velocity:**
- The change in velocity vector \( \Delta V = -10 \, \hat{i} - 10 \, \hat{j} \) points towards the southwest direction (since it has negative components in both the x and y directions).

### Final Answer:
The change in velocity of the scooter is approximately \( 14.14 \, \text{m/s} \) in the southwest direction.