A moves with `65km//h` while `B` is coming back of `A` with `80km//h`. The relative velocity of `B` with respect to `A` is

Options

A. `80km//h`
B. `60km//h`
C. `15km//h`
D. `145km//h`

Answer

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

### Step 1: Understand the velocities of A and B
- A is moving at a speed of 65 km/h.
- B is moving towards A (coming back) at a speed of 80 km/h.

### Step 2: Define the direction
- Let's assume A is moving in the positive direction (to the right).
- Since B is coming back towards A, we can consider B's velocity as negative in this context.

### Step 3: Write the velocities in vector form
- Velocity of A, \( V_A = +65 \, \text{km/h} \)
- Velocity of B, \( V_B = -80 \, \text{km/h} \) (since it is moving towards A)

### Step 4: Calculate the relative velocity of B with respect to A
The formula for relative velocity is:
\[ V_{B/A} = V_B - V_A \]
Substituting the values:
\[ V_{B/A} = (-80) - (65) \]

### Step 5: Perform the calculation
\[ V_{B/A} = -80 - 65 = -145 \, \text{km/h} \]

### Step 6: Interpret the result
The negative sign indicates that B is moving towards A at a speed of 145 km/h. However, since we are interested in the magnitude of the relative velocity, we can state:
\[ \text{Relative velocity of B with respect to A} = 145 \, \text{km/h} \]

### Final Answer
The relative velocity of B with respect to A is **145 km/h**.

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