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.

A 30 kg projectile moving horizontally with a velocity vecv_(0)=(120m/

1.	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.
Answer» Solution :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`