Example: You are traveling in a car (A) at 60 miles/hour east on a long straight road. The car (B) next to you is traveling at 65 miles/hour west. What is the speed of car B relative to car A?

Answer

To find the relative velocity of car B with respect to car A, we use the formula: V_BA = V_B - V_A. First, we define a coordinate system where east is the positive direction and west is the negative direction. The velocity of car A (V_A) is 60 mph east, which is +60 mph. The velocity of car B (V_B) is 65 mph west, which is -65 mph. Now, substitute these values into the relative velocity formula: V_BA = (-65 mph) - (+60 mph) = -125 mph. The negative sign indicates the direction is west. The question asks for the 'speed', which is the magnitude of the velocity. Therefore, the magnitude of the relative velocity is 125 mph. In simpler terms, because the cars are moving in opposite directions, their speeds add up from the perspective of an observer in one of the cars. 60 + 65 = 125 miles/hour.