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If Mr. E is aboard a spaceship traveling near the speed of light the usual reason for the spaceship not going faster than $c$ is the (relativistic) mass of the ship increases without bound, I think. Yet Mr. E says out loud what about the mass of the fuel? When the fuel's (relativistic) mass increases would its potential energy increase enough to compensate for the ship's (relativistic) mass increase?

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See relativistic rocket. –  David H Apr 12 at 3:39
Also a crucial point is that speeds are relative. From the referance frame of the rocket, it is not moving and it's mass is just it's normal rest mass. –  Punk_Physicist Apr 12 at 3:50
The other crucial point is that the actual reason for it not going faster than $c$ is the addition of velocity formula prevents you from accelerating above it –  Jim Apr 12 at 5:17
The actual reason for the rocket under consideration not going faster than $c$ (i.e. maximum signal speed) between a given starting gate and a given finish line is of course that the rocket also presents a signal having been sent from starting gate to finish line (and not even necessarily a signal of the highest speed). p.s. Concerning the well-known formula for adding speeds in the same direction it is worth noting that $\frac{u + v}{1 + u \, v} > 1$ for instance if $ v > 1 > u > 0$. –  user12262 Apr 12 at 20:44
Considering this situation if the mass of the ship increased relative to observers on Earth , would the mass of the fuel increase relative to the Earth observers, and subsequently would the potential energy of the fuel increase relative to Earth observers? –  user128932 Apr 15 at 5:42

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