How do I calculate the velocity of a two-ended rocket?

[haruspex]

Whoa, I just figured out the answer. The velocity of ##m_C## isn't ##v##, it's actually ##v-(\frac{m_R}{m_C})(v_R)##.

##v_{C}=v-(\frac{m_R}{m_C})(v_R)=\frac{3}{5}\frac{m}{s}-(\frac{2kg}{6kg})(\frac{9}{4}\frac{m}{s})=-\frac{3}{20}\frac{m}{s}##

Yes!

 

[Eclair_de_XII]

##t=2s##
##x_0=vt_1=\frac{12}{25}m##
##x_f=x_0+v_Ct=\frac{12}{25}m+(-\frac{3}{20}\frac{m}{s})(2s)=\frac{48-30}{100}m=\frac{9}{50}m##

Well, thank you very much for helping me through this, haruspex. I literally do not believe I could have figured this out without any sort of help. Thank you for always helping me.

 

[haruspex]

##t=2s##
##x_0=vt_1=\frac{12}{25}m##
##x_f=x_0+v_Ct=\frac{12}{25}m+(-\frac{3}{20}\frac{m}{s})(2s)=\frac{48-30}{100}m=\frac{9}{50}m##

Well, thank you very much for helping me through this, haruspex. I literally do not believe I could have figured this out without any sort of help. Thank you for always helping me.

You are welcome. But you could do it without help next time, right?

 

[Eclair_de_XII]

I think so. I'll see next weekend.