They both experience the same force because of the impact, due to the Newton's third law, like you say.
I think the question is not clear enough. If you assume there is no friction between the trucks and the ground, then you can use momentum considerations.
I know this shouldn't be an answer, but I'm new and I can't post a comment, yet.
Why do you want to know?
I'm not kidding. That's actually an important question. The answer really depends on what you intend to do with the information you are given.
Newton's laws are an empirical model. Newton ran a bunch of studies on how things moved, and found a small set of rules which could be used to predict what would happen to, say, a baseball flying through the air. The laws "work" because they are effective at predicting the universe.
When science justifies a statement such as "the rocket will go up," it does so using things that we assume are true. Newton's laws have a tremendous track record working for other objects, so it is highly likely they will work for this rocket as well.
As it turns out, Newton's laws aren't actually fundamental laws of the universe. When you learn about Relativity and Quantum Mechanics (QM), you will find that when you push nature to the extremes, Newton's laws aren't quite right. However, they are an extraordinarily good approximation of what really happens. So good that we often don't even take the time to justify using them unless we enter really strange environments (like the sub-atomic world where QM dominates).
Science is always built on top of the assumptions that we make, and it is always busily challenging those assumptions. If you had the mathematical background, I could demonstrate how Newton's Third Law can be explained as an approximation of QM as the size of the object gets large. However, in the end, you'd end up with a pile of mathematics and a burning question: "why does QMs work." All you do there is replace one question with another.
So where does that leave you? It depends on what you really want to know in the first place. One approach would simply be to accept that scientists say that Newton's Third Law works, because it's been tested. Another approach would be to learn a whole lot of extra math to learn why it works from a QM perspective. That just kicks the can down the road a bit until you can really tackle questions about QM.
The third option would be to go test it yourself. Science is built on scientists who didn't take the establishment's word at face value, went out, and proved it to themselves, right or wrong. Design your own experiment which shows Newton's Third Law works. Then go out there and try to come up with reasons it might not work. Test them. Most of the time, you'll find that the law holds up perfectly. When it doesn't hold up, come back here with your experiment, and we can help you learn how to explain the results you saw.
That's science. Science isn't about a classroom full of equations and homework assignments. It's about scientists questioning everything about their world, and then systematically testing it using the scientific method!
Best Answer
It sounds like you may have been confused because intuitively, you would think a reaction occurs after the action, in response to it. As you've found, that is not what Newton's third law is saying. The reaction force is not a response to the action. For this reason, some people don't like the statement "For every action, there is an equal and opposite reaction."
A better statement of Newton's third law is to say that forces always occur in pairs. It is impossible for object A to exert a force on object B without object B also exerting a force on object A. The two forces are simultaneous, of equal magnitude, and in opposite directions.
Mathematically, this is stated as
$$\mathbf{F}_{AB} = -\mathbf{F}_{BA}$$