To find the relative velocity of B with respect to A when they are moving in opposite directions, we can use the concept of vector addition.
Let's assume that A is moving to the right with velocity VA = V and B is moving to the left with velocity VB = 2V.
The velocity of B relative to A is given by the vector subtraction of VB from VA:
Velocity of B relative to A = VA - VB
Since A is moving to the right and B is moving to the left, their velocities have opposite directions. We can represent VA as a vector pointing to the right with magnitude V and VB as a vector pointing to the left with magnitude 2V.
Substituting the values into the equation, we have:
Velocity of B relative to A = V - (-2V)
When we subtract a negative quantity, it is equivalent to adding the positive quantity:
Velocity of B relative to A = V + 2V
Simplifying, we get:
Velocity of B relative to A = 3V
Therefore, the velocity of B relative to A when they are moving in opposite directions is 3V, pointing in the direction from B to A.