Question

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-60 m/s) and a second piece, also of mass m, moves with velocity (-60 m/s). The third piece has mass 3m.

Answer 1

Incomplete question as we have not told to find what.So the complete question is here

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-60 m/s)i and a second piece, also of mass m, moves with velocity (-60 m/s)j. The third piece has mass 3m.Just after the explosion, what are the (a) magnitude and (b) direction of the velocity of the third piece?

Answer:

`V_(3)=(20i+20j)m/s`

Step-by-step explanation:

Given data

The vessel at rest

Piece one,of mass m,moves with velocity=(-60 m/s)i

Piece two,of mass m,moves with velocity=(-60 m/s)j

Piece three,of mass 3m

As the linear momentum is conserved in this system,Because the system is closed and no external force acting on it

So momentum is given as

`p_(initial)=p_(final)`

As the vessel at rest so the initial momentum is zero

So

`m_(1)V_(1)+m_(2)V_(2)+m_(3)V_(3)=0\\m_(3)V_(3)=-m_(1)V_(1)-m_(2)V_(2)\\V_(3)=(-m_(1)V_(1)-m_(2)V_(2))/(m_(3)) \\V_(3)=(-m_(1)(-60m/s)i-m_(2)(-60m/s)j)/(3m)\\V_(3)=(20i+20j)m/s`