question_answer

A boy of mass 50 kg running at 5 m/s jumps onto a 20 kg trolley travelling in the same direction at 1.5 m/s. What is their common velocity?

Answer:

Boy (B)	Trolley (T)
\[{{m}_{B}}=50kg\]	\[{{m}_{T}}=20kg\]
\[{{u}_{B}}=5m/s\]	\[{{u}_{T}}=1.5m/s\]

\[{{v}_{B}}={{v}_{T}}=v=?\] According to the law of conservation of momentum, \[{{m}_{B}}{{u}_{B}}+{{m}_{T}}{{u}_{T}}={{m}_{B}}{{v}_{B}}+{{m}_{T}}{{v}_{T}}\] \[={{m}_{B}}v+{{m}_{T}}v\] \[\Rightarrow V=\frac{{{m}_{B}}{{u}_{B}}+{{m}_{T}}{{u}_{T}}}{{{m}_{B}}+{{m}_{T}}}\] \[=\frac{50\times 5+20\times 1.5}{50+20}=\frac{280}{70}=4m/s\]