In the discussion about calculating the final velocity of mass 1 in an elastic collision, participants analyze a scenario involving two masses, m1 and m2, with given speeds and angles. The key focus is on applying the conservation of momentum and correctly breaking down the momentum into x and y components. Participants struggle with the calculations and the appropriate use of equations for elastic collisions, particularly in determining the final velocity of m1 after the collision. The conversation emphasizes the importance of vector components in momentum and kinetic energy calculations, leading to a resolution of the kinetic energy lost during the collision. Ultimately, the correct approach involves separating the momentum components and applying the conservation laws accurately.