Consider two cases where the mass is moving with constant velocity (since both rockets are equal and in opposite directions) a) 2m/s and b)7m/s
Each rocket produces thrust by burning fuel (of negligible mass compared to M) that has some specific energy. Now I reason that the rate at which work is done on the mass M by the thrust of each rocket, should be equal to the rate at which energy of the rocket fuel is being consumed for conservation of energy.
(although the net work is zero, I'm talking about the work done by the thrust from each rocket, which should be non zero)
Since the thrust produced by the rockets on both cases a) and b) are the same, the rockets must be consuming fuel (and therefore energy) at the same rate on both cases.
power is given by Force$\times$velocity.
power of one rocket in case a) $5N\times2m/s=10W$
power of one rocket in case b) $5N\times7m/s=35W$
Now we have a situation where rate of work being done by the rockets are different for each case, but rate of consumption of fuel are equal for both cases. This seems to be a violation of conservation of energy.
Please help me clarify this.