Consider a system consisting of three particles:

m$1=5$ kg$,1=<10,-4,14>$ m$/$s

m$2=8$ kg$,2=<-12,8,-4>$ m$/$s

m$3=3$ kg$,3=<-23,38,22>$ m$/$s

$($a$)$ What is the total momentum of this system?

tot $=$

kg $$ m$/$s

$($b$)$ What is the velocity of the center of mass of this system?

cm $=$

m$/$s

$($c$)$ What is the total kinetic energy of this system?

Ktot $=$ J

$($d$)$ What is the translational kinetic energy of this system?

Ktrans $=$ J

$($e$)$ What is the kinetic energy of this system relative to the center of mass?

Krel $=$ J