$7)(25$ points$)$ A $4$ kg particle has a velocity of v$1=(4$i$20$t$$j$)$ m$/$s$,$ where t is the time

at some instant. A $3$ kg particle has a constant velocity of v$2=4$i m$/$s$.$ The initial

position of the $2$ kg particle is r$1=(1$i $+2$j$)$ m$.$ The initial position of the $3$ kg

particle is r$2=(3$i$2$j$)$ m$.$

a$)(6$ pts$)$ What is the initial x$-$component of the center of mass of this two$-$particle

system?

b$)(6$ pts$)$ What is the initial y$-$component of the center of mass of this two$-$particle

system?

c$)(7$ pts$)$ At t $=6$ s$,$ what is the velocity of the center of mass, vcm$?$ Don$$t forget

to include both components.

d$)(6$ pts$)$ What is the total momentum of the system Pcm of the system at t $=5$ s$?$