A particle of mass =6.50 kg moves with a velocity v1=x1i+y1j+z1k. A second particle of mass =3.50 kg moves with a velocity v2=x2i+y2j+z2k. And a third particle of mass =6.30 kg moves with a velocity v3=x3i+y3j+z3k. Here, (x1,y1,z1)=(-2.5,5.4,1.2), (x2,y2,z2)=(-2.3,0.1,-2.5) and (x3,y3,z3)=(3.3,-8.6,5.3).

Question

A particle of mass =6.50 kg moves with a velocity v1=x1i+y1j+z1k. A second particle of mass =3.50 kg moves with a velocity v2=x2i+y2j+z2k. And a third particle of mass =6.30 kg moves with a velocity v3=x3i+y3j+z3k. Here, (x1,y1,z1)=(-2.5,5.4,1.2), (x2,y2,z2)=(-2.3,0.1,-2.5) and (x3,y3,z3)=(3.3,-8.6,5.3). 
What is the magnitude of the velocity of the center of mass for the system?

bobpursley · Answer

the sum of the masses.
then multiply each of the velocities by the fraction ofmass it contains, ie, on v1= 6.50/totalmass*(-2.5,5.4,1.2), or
v1=(-.997, 2.15, .479)

after scaling each of the three velocities with the mass fraction, then add the like components of each to get Vcm