I'm trying to use this web site to make a DeltaV calculator but i've got stuck into calculating the velocity vector of the origin planet. Particulary i'm refering to the problem 5.6 described here where the velocity vector is given as VP = 25876.6X + 13759.5Y m/s. The problem is, how do i calculate it? I only know when i'm going to launch my spacecraft and from which planet. Of that planet i've already calculated the position vector. I haven't studied physics so if you can, keep it simple and, if you introduce new values, explain how to calculate them. Thanks!
If you're going between a planet and a moon of that planet, it's easiest to treat the planet as stationary. For planet to planet (or moon to moon) transfers within a system, if you don't need great accuracy, you can use circular orbit velocity (https://en.wikipedia.org/wiki/Circular_orbit#Velocity) as an approximation.
Complication increases rapidly beyond that. This paper is the best walk-through I've found for converting from Keplerian orbital elements to Cartesian position and velocity coordinates: https://downloads.rene-schwarz.com/download/M001-Keplerian_Orbit_Elements_to_Cartesian_State_Vectors.pdf -- it explains a great deal, but there are still some tricky bits.