Distance of two moving particles

[Oomph!]

Homework Statement

There are two particles. There are moving equally on two intersecting lines to intersection. On time t=0 is the distance of two particles d. The velocity of one particle relative to the other has a projection u in the direcion of d. In direction perpendicular to d is the projection v. The size of velocity of the particle relative to the other is V.

Task: find the shortest distance of particles and the time (r*,t*)
Answer: r*=dv/V; t*=du/V²

Homework Equations

; the attempt at a solution[/B]

V²=v² + u²

I think I have to find a function which expresses the distance of the particles in time. I have to find extreme of the function - the shortest distance. However, I don't know how create this function.

Please, could you tell me how can I solve this?

Thank you.

 

[mfb]

However, I don't know how create this function.

You can introduce a coordinate system. A good choice would be to have d aligned with one coordinate. What is the distance in this coordinate as function of time? What about the other coordinate?

 

[Oomph!]

Thanks. I found simplier solution where I don't need coordinates :)