Consider the motion of a rocket of mass $m$ in space with gas expelled at relative velocity $u$. I found two different version of writing the momentum of the system on Klepper Kolenkow and Morin book. Both agree about momentum of the system at the istant $t$.
While the difference is on the momentum at istant $t+dt$. On Morin I found:
While on Klepper Kolenkow it is claimed
The fact is: the mass $dm$ of gas is travelling at relative velocity $u$ with respect to the rocket. But is the rocket to be considered moving at velocity $v$ or $v+dv$ when writing the velocity of the gas?