If I remember correctly, an F-15 has a thrust ratio greater than the force of gravity, meaning it can accelerate straight up like a rocket.
Thrust/weight = 1.02
More important for this incident is that the large body generates substantial lift.
They can. I used to live about three miles from Lambert Field in St. Louis where McD built them. My friend was an engineer on the F-15s and would call me up to come out to the flight line to watch them test the aircraft. One day watching a pair of 15’s, they didn’t even get halfway down the runway and went vertical, straight up until you couldn’t see them anymore. Greatest fighter the US ever built (along with the F-18).