text: From what I understood in your question is that you have two objects (two frames of references), S and S'.\n\nEach 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.\n\nDiagram:\n\nS------S'\nS----S'\nS---S'\nS--S'\nS-S'\nSS'\n\nYour question did not mention that either object was travelig anywhere near the speed of light, so we can use ordinary Newtonain relativity for this.\n\nIt 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.\nWe know that the +y velocity is S (u) much eqaul the +y velocity of S' (v).  So we know that,\nv*cos(angle) = u\nor to rearrange,\ncos(angle) = u/v,\nso angle = cos^-1(u/v)