If the speed limit was lower than 50, then he would just write you for 50.
I once wrote a guy for 95 under similar circumstances.
I was driving over the Interstate overpass south of the town where I worked at 3-4 a.m. when I saw tailights go blazing by. I floored the gas pedal and turned onto the onramp and just left my foot on the floor for the 5 miles or so back to my jurisdiction. I still could not catch up.
I topped my vehicle out (127 or so) for several miles but I was barely able to keep the tailights in sight.
We went into my jurisdiction and were about to exit it when I had a stroke of luck (and the driver had misfortune).
One of the very few cars on the road changed lanes in front of him. I saw the brake lights come on, and I knew I had him. I did not hit my brakes or back off the gas until I was almost on top of him. I could now see that it was a minivan. I was in the far left lane, and the driver switched lanes in front of me and floored the gas.
When I looked at my speedometer, it was at 90 (this was after hitting the brakes). As the minivan accelerated, so did I. By the time I hit 95 mph, however, we were swiftly approaching my jurisdictional limit, so I leveled off at 95, watched the minivan increase the distance between us, and flipped on the blue lights.
I wrote the ticket.
The man shows up in court and defends on the theory that "My car won't go that fast." My presentation was something like what I wrote above. He was doing at least 95.
I actually felt sorry for him when the judge gave him 90 days in jail and a $1000 fine.
That particular municipal court judge really did not like people perjuring themselves.