1. The problem statement, all variables and given/known data A train is traveling in the x direction at a speed of v. On the train, a passenger is playing darts and fires a dart in the y direction with a speed of Uy. The dart hits the target and stops abruptly. What is the difference in the mass of the dart as observed by a person on the train versus an observer on the ground observing the dart as it hits the dart board? E = γu * m*c^2 Kinetic energy= energy moving - energy at rest = γu*m*c^2 - m*c^2 2. Relevant equations Is the initial mass of the dart (mass while flying) the same for the two observers? 3. The attempt at a solution Let S be the reference frame of the observer on the ground. S' is the reference frame of the observer in the train moving at v with the dart. Since the total energy of the flying dart is the same as when it stops in a reference frame, we can find the final mass in each frames. I get: final mass in S = [1-(Uy^2 + v^2)/c^2]^-1/2 * initial mass in S Final mass in s' = [1-Uy^2/c^2]^-1/2 * initial mass in S' I'm not sure if we can say that Initial mass in S ans initial mass in S' is the same. After that I guess I would get the answer by subtracting the final mass of S' with the final mass in S.