text: relativity theory? a pole is moving in a system s at y direction with the velocity u (in y direction). while moving it's parallel to the x axes (looks like a '-' that going up). a system s', which it's axes are parallel to those of s system, moves in a velocity v in x direction relatively to the s system. a viewr in s' system will find the pole moves while creating an angle with the x' axes (looks like '/'). what is the explanation of this angle, and how can i calculate the angle, using v and u (and maybe c - the light velocity) - pay attention that all velocities can be close to the light velocity. from what i understood in your question is that you have two objects (two frames of references), s and s'.  each are side by side, the first object is moving at a constant velocity, u, along the +y axis.  meanwhile, s' moves at a constant velocity, v, at some angle away away from the y axis in the +x direction such that s and s' stay parallel with eachother.  diagram:  s------s' s----s' s---s' s--s' s-s' ss'  your question did not mention that either object was travelig anywhere near the speed of light, so we can use ordinary newtonain relativity for this.  it is just common sense that since s' is moving at an angle away from s and yet stays parallel, it must be moving faster...but how much faster. we know that the +y velocity is s (u) much eqaul the +y velocity of s' (v).  so we know that, v*cos(angle) = u or to rearrange, cos(angle) = u/v, so angle = cos^-1(u/v)