1. The problem statement, all variables and given/known data The first part: find the x and y components of velocity U such that the particle fired with velocity U collides with the particle fired with velocity V. The second part: for a given d, what should V be to minimize U? 3. The attempt at a solution The first part is easy, I set t=v/g. This makes the x-component of U = d/t which = dg/v. Also, the y-component of U must be equal to V in order to collide with the V particle. The second part is causing a lot of trouble for me. I understand that if V is small, the x-component of the U velocity will be too large, and if V is large, the y-component of U will be too large, so there must be some intermediate velocity V that makes U minimal. I'm just having trouble expressing this with equations... any help?