True story.
Back in 1978 I had a new radio. The first hand held 2 Meter Ham Rig that was fully synthized. a Wilson WE-800 (2 meters is between TV carrier's 6 and 7).
Due to the Detroit Tigers playing a night game there was no way on earth I was going home at 11pm (Road blocked) so I decided to see what one watt into a "rubber Duck" antenna would do (About 1/4 watt effective I'm guessing)
I'm in Downtown Detroit (lodge Freeway s/b side between Porter and Howard)
The Repeater was in Allegan.
So you know there is a "Limit" to height is might but using a Mast Head Amplifier increases that limit.
What is the limit? Depends on the coax. the better the coax (lower loss) the higher the limit but at some point the added loss in the coax is greater than the added height gain..
I found several threads on the topic but due to the number of different grades of coax out there I don't have a calculator I can use to figure out the optimum height.
A ham from Windsor (Across the river from me) Tired, and failed, to join in he is running 10 watts into a 6DB gain antenna (40 Effective Radiated or 160 times the power I'm running) at 30 feet.
I made it, he did not. I could see his house from the 21's floor of the skyscraper my office was in.