Question

Related Rates: Iwhn the theory of relativity, an object that is travelling at an appreciable fraction of the speed of light has kinetic energy equal to mc^2((c/(sqrt(c^2-v^2)))-1) where m is the mass of the object, v its speed, and c is the speed of light (which is a constant). A miniture super rocket has a mass of 2kg and is currently travelling at 1/2 of the speed of light. It magically converts its mass into speed (conventional rockets do this by burning rocket fuel, which both pushes them forward and makes them lighter) so that its kinetic energy stays exactly the same. If the rocket wants to accelerate at 0.1c/second, how fast must it change mass?

Answer 1