Simple vector addition question

[vasiliy]

Two cars approaching each other with speed 100km/h each. Relative to one of the cars the road moves with the speed of 100km/h (car pulls it toward itself), the other car moves on the moving road, vectors add - relative velocity 200 km/h just the way it should be. Relative to the road two cars move with speed 100km/h, vectors point in opposite directions, add vectors, relative velocity equals 0. Why?? Changing system of coordinates should not matter, they both inertial. Galilean transformation does not work either the second car vector turns into 0. I don’t understand.

 

[jbriggs444]

The rule of Galilean velocity addition is that if B is moving with respect to A and C is moving with respect to B you take
$v_{ca} = v_{ba} + v_{cb}$

If you are in car A, the road B is moving 100km/h relative to you and car C is moving at 100 km/h relative to the road B then car C is moving 200 km/h relative to you.

Now place yourself on the road B. Car A is moving -100 km/h relative to you and car C is moving +100 km/h relative to you. The first question you need to ask is "what am I trying to calculate". If you are trying to calculate the velocity of car C relative to car A and you already know that car A is moving at -100 km/h relative to you then you have to flip the sign and conclude that you (along with road B) are moving at 100 km/h relative to car A. Now you are in a position to calculate $v_{ca} = v_{ba} + v_{cb} = 200 km/h$

 

[HallsofIvy]

You do not find the relative velocity between two objects by adding their velocity vectors (relative to some third system), you get the relative velocity by subtracting their velocity vectors.

 

[vasiliy]

That's it! All it took is one sentence - relative velocity Delta V= V1-V2, plain and simple. I was thinking about vector sum of forces but that's completely different story. Now it all makes sense. Thanks.