Question

A train is moving at a speed of 0.6c along the positive x-direction (don't worry about the unrealistic numerical values). A taxi is chasing the train at a speed of 0.4c along the positive x-direction. Both speeds are measured relative to the train station, which is at rest. (a) Use the velocity transformation formula to find the speed of the taxi, as measured by a passenger on the train. (1) Use the velocity transformation formula to find the speed of the train, as measured by the taxi driver. Clearly state, in both (a) and (b) which speeds play the role of u, u' and v, respectively, in the velocity transformation formula What would be the classical answer to questions (a) and (b)?

Answer 1

Velocity transformation formula is V^1 = V - U/1 - VU/C^2 We have to find V_C/T V_C/T = U - V/1 - UV/C^2 = 0.4C - 0.6C/1 - 0.4 times 0.6 C^2/C^2 = -0.2C/1 - 0.24 = -0.2C/0.76 = -0.263 C i.e observer in the train observes cas is at a speed of 0.263 C away from the train # Speed of train measured by Taxi driver V_T/C = V - U/1 - UV/C^2 = 0.6C - 0.4C/1 - 0.24C^2/C^2 = 0.2C/0.76 = 0.263C Just there is difference in dissection In classical mechanics Answer for past (A) would have been (0.4 - 0.6)C = 0.2C and past (B) would have been (0.6C - 0.4C) = 0.2C