A mass m is projected horizontally all along the x-axis having a velocity v towards a second object of mass a m, where 0 < a < 1. When the second mass consists of a velocity of -2v and the masses collide in such a way that they stick altogether after the collision. Supposing no external forces are acting, answer the given:
i) Determine the expression for the final velocity w after the collision.
ii) There exists a value of such that both masses come to rest after the collision. Prove or disprove.