questions,
(I tried to PM this response to you, but I don't think it went through -- I did not know you had started a thread. Anyway, here is my answer from the PM. Incidentally, I'm pretty certain I'm right about this -- it's basically a college freshman physics problem. There are various ways to complicate the problem taking into account air resistance, forward motion of the plane, etc.: your son will still turn out to be correct, although, unless he is a super-human jumper, his plan will only lessen the damage a bit.)
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Your son has an interesting question -- I had to think for a moment. I'd bet the kid ends up being a scientist or engineer!
His suggested action actually would help a little, if you jump at the right time.
One way to think about it is, say, the plane is falling down at 100mph. If your kid can jump upwards at 10 mph (relative to the plane of course), that means he will kill 10 mph of the 100 mph, and will therefore only be falling down at a speed of 90 mph. Still a bad situation, but not quite as bad.
Incidentally, this is the sort of question that occurs to me spontaneously -- I'm in an elevator, it jerks and I start getting nervous, I remind myself of all the modern fail-safe devices in elevators (they're very good), and then I start to think about what physics says I should do if the elevator were to fall.
Knowing how to ask good questions is a huge part of being good at science -- your son sounds as if he has the right kind of curiosity.
All the best,
Dave
