Perfectly inelastic collision
= Perfectly inelastic collision
A <perfectly inelastic collision> is an <inelastic collision> in which the bodies stick and share one outgoing <velocity>. For two isolated <point masses>, <momentum conservation> gives $v=(m_1u_1+m_2u_2)/(m_1+m_2)$. At fixed total <momentum>, common <velocity> minimizes the outgoing translational <kinetic energy>, so sticking gives the greatest loss of that <kinetic energy> for the specified incoming state.