A `30 kg` projectile moving horizontally with a velocity `vecv_(0)=(120m//s)hati` explodes into two fragments `A` and `B` of masses `12 kg` and `8 kg`, respectively. Taking point of explosion as origin and knowing that `3s` later position of fragment a is (`300m, 24m, -48m`), determine the position of fragment `B` at the instant.

Explanation

Initial corrdinates of `CM=(0,0,0)`
`x` coordinates of `CM` after `3 s`
`x_(CM)=120xx3=360m`
`y` coordinates of `CM` after `3s`,
`y_(CM)=-1/2"gt"^(2)=-45m`
After `3s`,
`(m_(1)+m_(2))x_(CM)=m_(1)x_(1)+m_(2)x_(2)`
`x_(2)=(30xx360-12xx300)/18=400m`
similarly `(m_(1)+m_(2))y_(CM)=m_(1)y_(1)+m_(2)y_(2)`
`=-30xx45=12xx24+18xy_(2)`
`y_(2)=-91m`
and in `z` coordinate `m_(1)z_(1)+m_(2)z_(2)=0implies z_(2)=32m`