Question 7.SP.38: What happens during inelastic impact?...

This is the case when one body absorbs the other or clings to it. Common sense indicates that they have a common final speed. Note that if e=0 is substituted into the equations for v_{1} and v_{2} in Problem 7.36, this is actually so:

v_{1}=\frac{m_{2} u_{2}  +  m_{1} u_{1}}{m_{2}  +  m_{1}} \quad v_{2}=\frac{m_{1} u_{1}  +  m_{2} u_{2}}{m_{2}  +  m_{1}} \quad \therefore v_{1}=v_{2}