I agree with batmom. There are already so many "simple" things (twist an ankle playing basketball, trip over the dog in the middle of the night) that possibly could lead to an injury you couldn't recover from before I Day, why add to the risk by doing something like sky diving? If you can't come in physically healthy on I Day, you'll be turned away and have to reapply next year. If you make it to I Day, take the oath, and get injured during BCT, there is a certain number of days you can miss (maybe 7? not sure) before getting turned back. A lot depends on when it happens during BCT (beginning vs. the end) and whether you can participate to some degree. Once you've taken the oath, if you get turned back, you will have a spot waiting for you (and won't have to reapply) the next year if you can physically rehab and be cleared medically.
My son had a dislocated shoulder a YEAR before BCT, rehabbed and was probably stronger than before, got DQ'd anyway, but received a waiver. He was told in the waiver letter that he would be evaluated at the start of In-Processing and might be sent home if they felt his shoulder wasn't strong enough (luckily he passed the eval with flying colors). But they are serious about basics coming in healthy and able to participate 100%!
Is it really worth the risk? You're so close now!
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Proud mom of a C3C