question_answer

A railway engine of mass 10,000 kg moving with a velocity of 2 m/s collides with a wagon of 20,000 kg at rest. After collision both move with the same velocity. Then find the common velocity.

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. \[{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}={{m}_{1}}v+{{m}_{2}}v\] \[\Rightarrow V=\frac{{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{(10,000\times 2)+(20,000\times 0)}{10,000+20,000}=0.66\,\,m/s\]