it is the same old 'light clock' thing (at least it is supposed to be), but I am trying to understand it in terms of a more mundane example. photons are claimed to have peculiar properties that tend to confuse things.

when the stationary observer sees the ball, if he is able to measure the speed of the ball, will it come out to the same speed as the person inside the train would measure...
does the fact that all actions inside the train appear to be moving slower cancel out the fact that the ball is traveling along a longer path? or would the measurement be achievable through some sort of vector addition (would vector addition result be the same as the straight measurement?)

eg. I clock the train at 50MPH. I know the maximum velocity for the ball is 200MPH and know this is it's current speed. I add the two vectors and come up with 206MPH [SQRT(200E2 + 50E2)]

what would I measure as the speed if I took a stopwatch and measured the time it takes to travel one cycle (assuming I know the distance between the plates and adjust the distance for the forward motion)?