Question

The reference frame K' moves in the positive direction of the x axis of the frame K with a relative velocity V. Suppose that at the moment when the origins of coordinates O and O' coincide, the clock readings at these points are equal to zero in both frames. Find the displacement velocity x of the point (in the frame K) at which the readings of the clocks of both reference frames will be permanently identical. Demonstrate that x < V.

Answer 1

Suppose x (t) is the locus of points in the frame K at which the readings of the clocks of both reference system are permanently identical then by Lorentz transformation 

(tan h θ is a monotonically increasing function of θ)