S = a stationary one-dimensional coordinate system. The x'-axis of another one-dimensional coordinate system S' coincides with the x-axis of S. S' moves along the x-axis of S in the direction of increasing x with velocity v. A ray of light is emitted from the origin of the moving system S' at the time t' = 0s to x' = 299,792,458m, arriving there at the time t' = 1s, and is reflected back to the origin, arriving there at the time t' = 2s.(adsbygoogle = window.adsbygoogle || []).push({});

x' = c*sqrt(1 - sq(t' - 1)) (1), where t' is in the closed interval [0s. 2s], describes the motion of the ray of light along the x'-axis of the moving system S' by the observer stationed on the x'-axis of the moving system S'.

x' = x - v*t (2), where t is in the closed interval [0s, 2s], describes the motion of the ray of light along the x'-axis of the moving system S' by the observer stationed on the x-axis of the stationary system S.

Adding each side of equation (1) to each side of equation (2) respectively, we get

2*x’ = c*sqrt(1 – sq(t’ – 1)) + x – v*t.

If x' = x = 299,792,458m, and

t' = t = 1s, then

v = 0m/s, provided we keep c constant.

If x' = 299,792,458m, and x = 299,822,258m, and

t' = t = 1s, then

v = 29,800m/s, provided we keep c constant.

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# X' relative to S' and relative to S

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