And your intuition is actually right! As a Gedankenexperiment: If you are on a train that moves 10 mph and you toss a ball to give it another 10 mph of veloci

And your intuition is actually right! As a Gedankenexperiment: If you are on a train that moves 10 mph and you toss a ball to give it another 10 mph of velocity (relative to the train), your arms need to perform the same amount of work on the moving train as on a stationary train.