Question

A train car, initially traveling at 90 m/s approaches 3 identical coupled train cars, which are initially at rest. The moving train hitches to the stationary train cars, and they all move off together. What is their final speed (in m/s)?

Answer 1

22.5 m/s

Step-by-step explanation

This is a perfectly inelastic collision, so momentum is conserved:

`m_1v_(o1)+m_2v_(o2)=m_1v_f+m_2v_f`

The final speed is the same for both. All the cars have the same mass, so m1 = m, and m2 = 3m - it's 3 times the mass, because they are 3 cars. Also the initial speed of m2 is 0, because the cars are at rest:

`\begin{gathered} m\cdot90+3m\cdot0=4m\cdot v_f \\ 90m=4m\cdot v_f \end{gathered}`

Solving for vf:

`v_f=(90m)/(4m)=(90)/(4)=22.5`

Their final speed is 22.5 m/s