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m_{1i}v_{1i}^2 &= m_1\left(\frac{m_1v_{1i}-m_2v_{2f}}{m_1}\right)^2 + m_2v_{2f}^2\ &=\frac{1}{m_1}(m_1^2v_{1i}^2-2m_1v_{1i}m_2v_{2f}+m_2^2v_{2f}^2)+m_2v_{2f}^2%0
\[ m_{1i}v_{1i}^2 &= m_1\left(\frac{m_1v_{1i}-m_2v_{2f}}{m_1}\right)^2 + m_2v_{2f}^2\ &=\frac{1}{m_1}(m_1^2v_{1i}^2-2m_1v_{1i}m_2v_{2f}+m_2^2v_{2f}^2)+m_2v_{2f}^2%0 \] \gamma = 1
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