Two objects A and B are moving in opposite directions with velocities `v_(A) and v_(B)` respectively, the magnitude of relative velocity of A w.r.t. B is

Options

A. `v_(A)-v_(B)`
B. `v_(A)+v_(B)`
C. `v_(B)-v_(A)`
D. `v_(A)//v_(B)`

Answer

To find the magnitude of the relative velocity of object A with respect to object B, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Direction of Velocities**:
- Let the velocity of object A be \( v_A \) in one direction (let's say to the right).
- Let the velocity of object B be \( v_B \) in the opposite direction (to the left).

2. **Define the Relative Velocity**:
- The relative velocity of object A with respect to object B is defined as:
\[ v_{AB} = v_A - v_B \]
- Here, \( v_{AB} \) is the velocity of A with respect to B.

3. **Account for the Opposite Directions**:
- Since A and B are moving in opposite directions, we can express the velocity of B as negative:
\[ v_B = -v_B \]
- Therefore, the equation for relative velocity becomes:
\[ v_{AB} = v_A - (-v_B) = v_A + v_B \]

4. **Magnitude of the Relative Velocity**:
- The magnitude of the relative velocity is simply the absolute value of \( v_{AB} \):
\[ |v_{AB}| = |v_A + v_B| \]

5. **Final Expression**:
- Thus, the magnitude of the relative velocity of A with respect to B is:
\[ |v_{AB}| = v_A + v_B \]

### Summary:
The magnitude of the relative velocity of object A with respect to object B, when they are moving in opposite directions, is given by:
\[ |v_{AB}| = v_A + v_B \]