Answer:
\[{{m}_{1}}=10,00\,kg,\,\,{{u}_{1}}=2m/s\]
\[{{m}_{2}}=20,000\,\,kg,\,\,{{u}_{2}}=0\,\,(at\,\,rest)\]
Final velocity of the rail engine \[{{V}_{1}}={{V}_{2}}=V\]
Using law of conservation of momentum.
\[{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}={{m}_{1}}v+{{m}_{2}}v\]
\[\Rightarrow V=\frac{{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]
\[=\frac{(10,000\times 2)+(20,000\times 0)}{10,000+20,000}=0.66\,\,m/s\]
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