Find the velocity of `c.m.`

Explanation

`(v_(c.m.))_(x) = ( 2m ( 5v_(0) cos 37^(@))+ 3 m v_(0))/(m + 2m + 3m = 6m) = (11 v_(0))/(6)`
`(v_(c.m.))_(y) = (mv_(0) + 2m (5v_(0) sin 37^(@)))/(m + 2m + 3m) = ( 7v_(0))/(6)`
`vec(v)_(c.m) = (v_(c.m.))_(x) + (v_(c.m.))_(y) hat(j) = ( 11 v_(0))/(6) hat(i)+(7v_(0))/(6) hat(j)`
`v_(c.m.) = sqrt(((11v_(0))/(6))^(2) + ((7v_(0))/(6))^(2)) = (v_(0))/(6) sqrt(170)`
`tan theta = ( 7 v_(0)//6)/(11v_(0)//6)=(7)/(11) rArr theta = tan^(-1) ((7)/(11))`
OR
`m_(1) = m , vec(v)_(1) = v_(0) hat(j)`
`m_(2) = 2m , vec(v)_(2) = ( 5 v_(0) cos 37^(@)) hat(i) + ( 5 v_(0) sin 37^(@)) hat(j)`
`= 4 v_(0) hat(i) + 3 v_(0) hat(j)`
`m_(3) = 3m , vec(v)_(3) = v_(0) hat(i)`
`vec(v)_(c.m.) = (m_(1) vec(v)_(1) + m_(2)vec(v)_(2) + m_(3)vec(v)_(3))/(m_(1) + m_(2) + m_(3))=(11 v_(0) hat(i) + 7 v_(0) hat(j))/(6)`
`= (11v_(0))/(6) hat(i) + (7v_(0))/(6) hat(j)`