Up here in Alaska there was some kid a few years ago who thought it would be cool to build a guided missile. His dad thought so too (now your expecting me to say that Donald Rumsfeld showed up at his door in person) so his dad paid for it, and this kid built some guided missiles to shoot down remote control planes. And no one had any problem with it at all, because he didnt try to hide it or anything, he just did it, was successful (the local paper thought correctly that he was some kind of genius) and became a bit of a legend. Please note that im doing this story for memory so im kinda vague on the details.
As for doing the project I would say have at it. Probably the easiest thing you could do would be to track the rocket from the ground and collect data on its flight path and such. You could either put a beacon on the rocket, or use a camera. If you want to actually control the rocket whatever you do dont put FIRST stuff on it. FIRST stuff is ok as far as use in a competition where it is necessary for the officials to have an incredible amount of control over the machine, but it is bulky, slow, and because of its requirement for a radio link it isnt really what you want, in addition to being way too expensive. Get a few PIC micros, a programmer, and have at it. Total cost= less than a quarter of a FIRST control system, assuming you have to buy a compiler and a programmer. If you want to save money and have more fun make them learn assembly
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