Hi everyone. I'll be grateful if someone can help me with this problem. 1. The problem statement, all variables and given/known data I have a closed system composed of one particle. The maximal velocity that this particle can have is equal to Vc. Here we consider only 2D space: X and Y direction. The particle velocity is V (which is limited to Vc) and have two velocity components Vx and Vy, each cab vary from 0 to Vc. The existence of Vc creates the relation between Vx and Vy. For example if Vx = Vc then Vy = 0. We can write this relation as follows: Vx2 + Vy2 ≤ Vc2. I want to express the component Vy as a function of Vx. 2. The attempt at a solution In order to resolve this, first I studied the case when the overall velocity V is equal to Vc. In this case: Vx2 + Vy2 = Vc2. Then, Vy = sqrt( Vc2 - Vx2) . (1) Can I conclude that this last relation (1) is correct for all cases (and not only when V = Vc)? My problem is that I don't know if it is mathematically justified to take a special case: V = Vc and then conclude that the final relation (1) between Vy and Vx works for general case for any value of V.