Inelastic Collision
Objects collide and stick together, momentum is conserved but not kinetic energy
Elastic Collision
Objects collide and bounce off, momentum is conserved and so is kinetic energy
Velocity of mass 1 after an inelastic collision
v_1f = v_2f = (m_1v_1 + m_2v_2)/(m_1 + m_2)
Velocity of mass 1 after an elastic collision
v_1f = (v_1i)(m_1 - m_2)/(m_1 + m_2) + (v_2i)(2m_2)/(m_1 + m_2)