There are a few UFO videos that are shot from a moving helicopter (or plane) where the camera tracks what seems to be a fast moving object. The best demonstration of this effect now comes from Tom Churchill of Churchill Navigation with this video of a mylar balloon filmed from a helicopter. After the cameraman starts tracking the balloon it looks like it's moving incredibly fast over the background, but we can see it's just a balloon drifting in the wind, and the apparent motion comes from a combination of the helicopter motion, and the magnified movement due to the zoom factor.
With just a little math we can find out where the balloon is relative to the helicopter, and discover that it's not actually moving very fast at all! Thanks to Churchill Navigation for permission to use this video! The original is here:
Note: the "Go Fast" video was shot from a jet, not a helicopter, but the point still stands. Much analysis of that video can be found here: