Jet pack endurance is much longer than 15 seconds these days. Some of the winged packs could do it with ease.
Take a look at some of them on YouTube.
No reason not to hit those altitudes with one if someone has the cojones to do it.
Based on a limited investigation, I agree, it's possible.
What I don't understand is why some "idiot" would do such a stunt on the flight path of a major airport endangering themselves and the lives of all those on passenger aircraft. I was involved in a "near miss" close encounter with a home made/powered hang glider once at a small airport in Oklahoma once. Scared the "puddin" out of me. He was just out doing his thing and had no idea a flight of nine Army helicopters were coming in for refuel.
Ironically, he didn't learn much from our close encounter. Although he did land at the same airport, he was still screwing around and got his ass blown topsy turvy when the Chinooks came in. We tried to warn him but, he didn't even have a radio. Shrug.
Ya can't fix stupid.
Rams