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. `20.0ms^(-1)` south eastern direction
B. zero
C. `10.0ms^(-1)` in southern direction
D. `14.14ms^(-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, we can follow these steps:

### Step-by-Step Solution:

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

2. **Determine Final Velocity**:
After making a right turn of 90 degrees, the scooter will be moving due south with the same speed. Thus, the final velocity is \( V_2 = 10 \, \text{m/s} \) directed south.

3. **Express Velocities as Vectors**:
- The initial velocity vector \( V_1 \) can be represented as \( V_1 = 10 \hat{i} \) (where \( \hat{i} \) is the unit vector in the east direction).
- The final velocity vector \( V_2 \) can be represented as \( V_2 = -10 \hat{j} \) (where \( \hat{j} \) is the unit vector in the south direction).

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

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

6. **Calculate Numerical Value**:
The numerical value of \( 10\sqrt{2} \) is approximately:
\[ 10\sqrt{2} \approx 10 \times 1.41 \approx 14.14 \, \text{m/s} \]

7. **Direction of Change in Velocity**:
The direction of the change in velocity vector \( \Delta V \) can be determined using the angle it makes with the axes. Since it has equal components in the negative \( \hat{i} \) and negative \( \hat{j} \) directions, the direction is southwest.

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

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