Question

Two bodies of masses `10 kg and 2 kg` are moving with velocities `(2 hati - 7 hatj + 3hat k) and (-10 hati + 35 hatj - 3hatk) m//s` respectively. Calculate the velocity of their centre of mass.

Answer 1

Here, `m_(1) = 10 kg, m_(2) = 2 kg`
`oversetrarr(v_(1)) = (2 hati - 7 hatj + 3hatk) , overset rarr(v_(2)) = (-10 hati + 35 hatj - 3hatk)`
`oversetrarr(v_(cm)) = (m_(1) oversetrarr(v_(1)) + m_(2) overset rarr(v_(2)))/(m_(1) + m_(2))`
`=(10(2 hati - 7 hatj + 3 hatk) + 2 (-10 hati + 35 hatj - 3 hatk))/(10 + 2)`
`=(24 hatk)/(12) = 2 hatk ms^(-1)`