Still, it seems to me that of all things a fighter pilot would be skilled at, being able to judge the distance to - and speed of - objects in the sky around them would be near the top of their list. It's pretty much what they do.Because, when you approach a roughly-stationary object at 1100mph, it can seem to suddenly appear behind you... or zip below you... or just over your head. Furthermore, your concept of speed is skewed when the ground 10,000 feet below you is your only reference. All of a sudden a stationary balloon seems to be moving unbelievably fast!
And no, I don't believe fighter pilots chase balloons as part of their normal training. They usually chase other objects of comparable speed.