b) Collisions in two dimensions
a) the principle of conservation of momentum
b) collisions and interaction of bodies in one dimension and in two dimensions
principle of the conservation of momentum → total momentum before a collision = total momentum after the collision

p1² = p2² + p3²
(total initial momentum of mass 1 and 2)² = (total final momentum of mass 1)² + (total final momentum of mass 2)²

total momentum in the x-direction
m1v1 = (m1)(v2cosθ1) + (m2)(v3cosθ2)
total momentum in the y-direction
m1v1 = (m1)(v2sinθ1) + (m2)(v3sinθ2)