Nice try, stupid.
"A box is divided into two parts by a wall …"
Ever heard of systems with two (or more) "Inertial frames of reference" (which one box is not)?
Also conveniently left out impulse p=m x v (what actually drives a rocket, same equation for a "terrestrial" rocket, as in outer space) …
But then you probably never build a rocket yourself, or simulated one. What's next? Flat Earth, right?
Trying to tell Anons to think – lol. Better you should start doing that yourself.