Huh? I never said anything about a balloon. I'm talking about the helicopter that was mention in the OP.
What if the train was already moving and then you made it take off. Does it now hover in that space? I would say yes. Would it continue to hover in that space or start to go backwards?
Once it lifted off, the same result would happen. Whether it actually "moves" or not would depend on your perspective (if you are comparing the helicopter's position relative to the train, or to the Earth). In either case, once it lifted off, it would maintain its position relative to the Earth, until it smacked against the back wall of the train.
If the airflow on the train is stagnant I think the helicopter stays stationary. If the windows were open, then I would agree. Otherwise, can you imagine your dropped something when flying a commercial airliner. Splat 550mph into the back wall. Am I wrong. Is it all dependent upon airflow?
If you fly it while sitting in the van, you'll end up involuntarily "cheating" by hovering relative to your visual references inside the van. You need a transparent van and a friend outside taking off when you drive by him.
In a sealed, moving car, if you make it take off and hover, it is going to move with the car, it will not stay in the same place relative to the earth. In the problem described, with both objects stationary relative to the earth, the train will move away while the helicopter does not, so the rear of the train car will get closer to the helicopter. Whether or not it will hit the rear wall depends on factors we don't know.
I don't think this is right... It would already have the forward inertia because it and the train are moving forward when it takes off... Would it then lose momentum and slowly move to the back of the train or stay where it is relative to the train? I'm now remembering why I hated my modern physics class... this makes my brain hurt.
It would have momentum, but would lose the "driving force". It wouldn't come to a screeching halt as soon as it lifted off, but it would start to slow down and eventually start moving backwards (relative to the train). This is assuming the pilot only takes it vertical.
Hang on, was it ever confirmed that the windows on the train are open, and the train isn't completely sealed off?
Does it need a driving force? An object in motion will stay in motion... assuming the windows are closed, the air in the train is also moving at the speed of the train, so the helicopter would just hover right were it lifted off until the train changed speeds right?
I wasn't working off the assumption that the train was sealed (this whole time). That's why I made that post asking for clarification about the windows. I thought earlier someone said the windows were open.
The original description says the doors close, and the train takes off. I don't think the windows pre operable in that type of train, outside of an emergency.
Just to add some more fun to the mix: In forward flight with a helicopter: Does the advancing or retreating blade provide the lift for forward motion? (Advancing meaning the blade as it is rotating with the direction of travel) Assume a two-bladed rotor for simplicity.
No. It would maintain it's vector, assuming ideal air stability. Newton covered all of this in laws 1 2 and 3.