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

ANSWER

22.5 m/s

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:

$v_f=\frac{90m}{4m}=\frac{90}{4}=22.5$

Their final speed is 22.5 m/s