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)