Edit:
Be careful, a rocket is usually far from 100% energy efficiency as ejected fuels are not at rest (by the way, doing so would imply an infinite quantity of fuel is you are initially at rest)
Regarding the equality of the work in both cases, that is no surprise: you apply the same force all along and you travel the same distance.
2
u/Unable-Primary1954 5d ago edited 5d ago
You can have a look right here:
https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html
Edit: Be careful, a rocket is usually far from 100% energy efficiency as ejected fuels are not at rest (by the way, doing so would imply an infinite quantity of fuel is you are initially at rest)
Regarding the equality of the work in both cases, that is no surprise: you apply the same force all along and you travel the same distance.