Newton's Cradle

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PDF of Equation Derivation
\[v_{f1} = \frac{m_{1}\cdot v_{i1} - m_{2} \cdot e \cdot v_{i1}}{m_{1} + m_{2}} \; \mathrm{m/s} \qquad v_{f2} = \frac{m_{1}\cdot v_{i1} + m_{1} \cdot e \cdot v_{i1}}{m_{1} + m_{2}} \; \mathrm{m/s}\]

Free Body Diagram of First Collision: