Understanding about momentum

[DrVirus]

this problem needs alittle understanding about momentum, something i don't understand that much.

A ball of mass 600g is moving 12 m/s[e]. The ball suddenly explodes into three equal mass pieces. One piece heads north at 6m/s, the second piece heads west at 5m/s. Determine the velocity of the third piece.

Can someone please show the calculations for me please, thnx alot.

 

[HallsofIvy]

Pretty straight forward. The initial velocity is <12, 0> (I'm taking my axes to point east and north). The intitial momentum vector is (mass times velocity) 0.6 KG <12 m/s, 0> = <7.2, 0>.

After the "explosion", each piece has mass 200 mg= 0.2 kg. The piece heading north at 6 m/s has momentum .2<0, 6>= <0, 1.2>. The piece heading west at 5 m/s has momentum .2<-0.5, 0>= <-0.1, 0>.
If we let <x, y> be the velocity of the third piece, its momentum is
<.2x, .2y>.

Conservation of momentum says: <7.2, 0>= <0- 0.1+ 0.2x, 1.2+ 0+ .2y> or 0.2x- .1= 7.2 and 0.2y+ 1.2= 0.