Jamaal Charles Passes to Himself - Real or Fake?

There's a video of Kansas City Chief running back Jamaal Charles in Pumas catching his own 45 yard pass. 

This is a pretty awesome feat for anyone, including NFL players.  Charles is one of the best backs in the NFL and (as a former track star) a very fast guy, but since we never saw the ball actually leave his hand, nor did we see it in flight until he catches it, could it have been faked?  Is it actually possible for him to have caught his own pass 45 yards down the field?  This isn't a feat made to look obviously fake, like Michael Vick throwing a ball out of the stadium, but is something that is in the realm of possibility.  Let’s look at the physics behind what he did.

There are two factors to look at in determining whether this feat is possible or not.  Can Charles realistically run that fast and can Charles throw that ball that high and far?

Let's see if our analysis can help determine if this is possible or not.  Warning, lots of math ahead!