collision.txt

Cr = (v_ball - v_cue) / (u_cue - 0)     ... (by definition of Cr)

so,
v_ball = Cr·u_cue + v_cue         ... [1]

m_cue·u_cue + m_ball·0 = m_cue·v_cue + m_ball·v_ball     ... (conservation of momentum)

so,
v_cue = (m_cue·u_cue - m_ball·v_ball) / m_cue
      = u_cue - v_ball (m_ball / m_cue)

      
Plugging v_cue into equation [1]
v_ball = Cr·u_cue + u_cue - v_ball (m_ball / m_cue)

v_ball (1 + m_ball / m_cue)  = u_cue (Cr + 1)

v_ball / u_cue = (Cr + 1) / (1 + m_ball / m_cue)