Two bodies of masses 10 kg and 2kg

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Two bodies of masses 10 kg and 2 kg are moving with velocities 2 i 7 j +3 k and 10 i +35 j 3 k m / s respectively. Find the velocity of the centre of mass of the system.

Solution

m1=10kg m2=2 kg V1=2i-7j+3k m/s V2=-10i+35j-3k m/s Velocity of center of mass= (m1v1+m2v2)/(m1+m2) =[10(2i-7j+3k)+2(-10i+35j-3k)]/(10+2) =(20i-70j+30k-20i+70j-6k)/12 =(0i+0j+24k)/12
=24k/12=2k.

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