I want to ask something with the fear of sound silly to most of you.

A)Let's say we have two identical rockets and the air resistance is excluded.
The first rocket travels upwards with 100mph while the second travels upwards with 50mph.It's obvious that after an hour the faster rocket will have produced double work.Does this mean that it will have used double fuels?
As far as I understand it since both the rockets move with constant speed they exert the same and equal with their weight force for an hour.Isn't logical to conclude that since both the rockets use the same force for the same duration they use the same fuels too?

Dear nitin,

You have a situation where the thrust of the rocket is precisely equal to it's weight so that it proceeds with whatever initial velocity it is given.

All that the rocket engine is doing in both cases is to balance the weight, it is not doing any work because it is not moving the rocket. The movement of the rocket is entirely a consequence of it's initial velocity. In Newtonian terms it 'proceeds in it's state of rest or uniform motion in a straight line'. It's exactly as if the rocket were not moving, simply hovering.
In a sense, both rockets are simply wasting fuel.

In reality, rockets do not move with uniform velocity, they accelerate and since F=ma, work is done and turned into kinetic energy.

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All the best.

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