Vector applications question – Elastic collision, momentum, and kinetic energy

For those of you who want a bit of a challenge with vectors – here is a modelling and problem solving question that involves the concept of conservation of momentum mixed with vectors as well as conservation of kinetic energies. Must be okay with understanding the difference between vector and scalar quantities and finding the horizontal and vertical component of vectors before continuing with this question. Lots of simultaneous equation solving as well. Have fun with it!