Anoop is moving due east with a velocity of `1 m//s` and Dhyani is moving due west with a velocity of `2 m//s.` what is the velocity of Anoop with respect to Dhyani?

Explanation

To find the velocity of Anoop with respect to Dhyani, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Directions and Velocities:**
- Anoop is moving due east with a velocity of \(1 \, \text{m/s}\).
- Dhyani is moving due west with a velocity of \(2 \, \text{m/s}\).

2. **Assign Positive and Negative Directions:**
- Let's choose east as the positive direction and west as the negative direction.
- Therefore, we can represent Anoop's velocity as:
\[ v_A = +1 \, \text{m/s} \]
- Dhyani's velocity, moving west, will be represented as:
\[ v_D = -2 \, \text{m/s} \]

3. **Calculate the Relative Velocity:**
- The velocity of Anoop with respect to Dhyani (\(v_{A/D}\)) can be calculated using the formula:
\[ v_{A/D} = v_A - v_D \]
- Substituting the values we have:
\[ v_{A/D} = 1 - (-2) \]

4. **Simplify the Expression:**
- This simplifies to:
\[ v_{A/D} = 1 + 2 = 3 \, \text{m/s} \]

5. **Determine the Direction:**
- Since the result is positive, it indicates that the velocity of Anoop with respect to Dhyani is towards the east.
- Therefore, we conclude:
\[ v_{A/D} = 3 \, \text{m/s} \, \text{due east} \]

### Final Answer:
The velocity of Anoop with respect to Dhyani is \(3 \, \text{m/s}\) due east.

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