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 1: Define the velocities
Let:
- \( v_A \) = velocity of object A (moving in the positive x-direction)
- \( v_B \) = velocity of object B (moving in the negative x-direction)

### Step 2: Assign signs to the velocities
Since object A is moving in the positive direction, we can represent its velocity as:
- \( v_A = +v_A \)

Object B is moving in the opposite direction, so we represent its velocity as:
- \( v_B = -v_B \)

### Step 3: Write the formula for relative velocity
The relative velocity of object A with respect to object B is given by the formula:
\[ v_{AB} = v_A - v_B \]

### Step 4: Substitute the values
Now, substituting the values of \( v_A \) and \( v_B \) into the equation:
\[ v_{AB} = v_A - (-v_B) \]
This simplifies to:
\[ v_{AB} = v_A + v_B \]

### Step 5: Determine the magnitude
Since we are interested in the magnitude of the relative velocity, we can express it as:
\[ |v_{AB}| = v_A + v_B \]

### Conclusion
Thus, the magnitude of the relative velocity of A with respect to B is:
\[ |v_{AB}| = v_A + v_B \]