The laws of conservation of momentum and energy state that they will stay the same before and after both collisions. Part of the momentum and energy is converted into heat which is in effect molecular velocity in the bodies involved. One of the details that you left out was the masses of both cars. For instance, if the mass of the car in the first incident is twice the mass of the other car then its momentum would be p1 = m1 x 100 = 2 x m2 x 100 = m2 x 200 and the momentum of the other car is p2 = m2 x 50 so that the momentum of the first car is four times greater than the second when hitting the wall and all that extra energy has to go somewhere both into heat and damage. In the second case with each other you have, p1 = m1 x 50 = 2 x m2 x 50 = m2 x 100 for the first car and p2 = -50 x m2 which is half the momentum of the first car but in the opposite direction. After the collision the net result is 50 x m2 in the direction of the bigger car minus any energy loss during the collision with the end result better determined by experimentation with possibly slightly differing results each time. But then again this is not a relative motion problem because if involves acceleration or rather deceleration.Can the above explain an anomaly I've never understood?
A car drives at 100 mph into an immovable object. You can imagine the mess the car is in.
Another car drives at 50 mph into an immovable object. Obviously, the car is a mess - but nowhere near as bad a mess as the 100 mph car.
Two cars drive straight at each other at 50 mph. Relative to each other, they are travelling at 100 mph. When they collide, will the damage to the cards be approximately equivalent to the 100 mph car above, or the 50 mph car above?