A train is moving with a speed of 0.9c, when a laser is fired upwards inside the train to calculate the time of the laser movement of 1m, what is the distance that an observer on the ground will observe the laser movement?

t = * t0 t 2.294 * (1m / c)

d_vertical = c * t c * 2.294 * (1m / c) 2.294m

d_horizontal = v * t = 0.9c * 2.294 * (1m / c) 2.0646m

d_total = sqrt(d_horizontal + d_vertical) d_total = sqrt((2.0646m) + (2.294m)) 3.061m

The question is ; why do we need to consider the horizontal distance and if we do consider will the relative speed to the ground greater than c which is not true?