question_answer

A truck of mass 500 kg moving at 4 m/s collides with another truck of mass 1500 kg moving in the same direction at 2 m/s. What is their common velocity just after the collision if they move together?

Answer:

Truck \[({{T}_{1}})\]	Truck \[({{T}_{2}})\]
\[{{m}_{{{T}_{1}}}}=500kg\]	\[{{m}_{{{T}_{2}}}}=1500kg\]
\[{{u}_{{{T}_{1}}}}=4m/s\]	\[{{u}_{{{T}_{2}}}}=2m/s\]
\[{{V}_{{{T}_{1}}}}={{V}_{{{T}_{2}}}}=V=?\]

  \[{{m}_{{{T}_{1}}}}{{u}_{{{T}_{1}}}}+{{m}_{{{T}_{2}}}}{{u}_{{{T}_{2}}}}={{m}_{{{T}_{1}}}}{{v}_{{{T}_{1}}}}+{{m}_{{{T}_{2}}}}{{v}_{{{T}_{2}}}}\] \[{{m}_{{{T}_{1}}}}{{u}_{{{T}_{1}}}}+{{m}_{{{T}_{2}}}}{{u}_{{{T}_{2}}}}={{m}_{{{T}_{1}}}}v+{{m}_{{{T}_{2}}}}v\] \[\Rightarrow V=\frac{{{m}_{{{T}_{1}}}}{{u}_{{{T}_{1}}}}+{{m}_{{{T}_{2}}}}{{u}_{{{T}_{2}}}}}{{{m}_{{{T}_{1}}}}{{m}_{{{T}_{2}}}}}\] \[=\frac{5004+1500\times 2}{500+1500}=\frac{2000+3000}{2000}\] \[=\frac{5000}{2000}=2.5m/s\]