RC car speeds is really fast. It's definately easier at "slow walking speeds" like 30cm/sec. RC car speeds would basically be building missiles lol except you have the added challenge that the chaser can't actually impact the leader. I'm going to guess this is only for horizontal surfaces right? With little elevations and hills then one vehicle might lose track of the other unless it had something like a pan-tilt sensor head to allow the vehicle to look around without actually moving the vehicle (or just make the sensors have a really wide field of view vertically and horizontally.
Getting it to follow at a distance of a few inches at speeds of 50km/h has a bunch of problems. A big one being that even if you had something that could follow that closely, it would never be able to stop in time to not collide with the leader- somewhat of a problem since any maneuver would make the leader slow down (ever heard of tailgating?). Slowing things down is the best thing you can do to make this easier.
The faster you go, the larger spacing between the two vehicles you need. I can see why you want inch spacing though because you are following around obstacles and you need the distance close enough so the chaser can blindly follow the leader and not need to "think" about how to catch up with the leader.
Personally, I think something vision-esque is needed (with IR being the simplest). Heatseeking works too but those are harder to pull off and easier to fool. You could get a CMUCam or some other hobbiest vision camera system and apply an IR filter to it and get use the onboard processor to calculate the centroid of the image which will probably be the IR beacon on the lead vehicle. CMUCams are really cheap for hobbiests, but if you are on a school project budget then they might take up 50% of your budget.
So in that case, a manual array of IR detectors is what you have to use (like Duffy).