m₁/m₂=3 -> m₁=3m₂
p₁=p₂
p=mv -> v=p/m
[tex]E_k=\frac{mv^2}{2}=\frac{m(\frac{p}{m})^2}{2}=\frac{\frac{p^2}{m}}{2}=\frac{p^2}{2m}[/tex]
[tex]E_k_1=\frac{p^2}{2m_1}=\frac{p^2}{2*3m_2}=\frac{p^2}{6m_2} \\ \\E_k_2=\frac{p^2}{2m_2}[/tex]
[tex]\frac{E_k_1}{E_k_2}=\frac{\frac{p^2}{6m_2}}{\frac{p^2}{2m_2}}=\frac{p^2}{6m_2}*\frac{2m_2}{p^2}=\frac{2}{6}=\frac{1}{3}\\ \\E_k_2=3E_k_1[/tex]
