To solve this problem we will use the concepts related to the conservation of the Momentum. From finding the changes at the initial and final moment we will have the value of the components of the pieces after the explosion. Let's start:
[tex]\vec{p_e} = \vec{p_{A}}+\vec{p_{B}}[/tex]
Where,
[tex]\vec_{p_e} =[/tex] Momentum of the object before explosion
[tex]\vec{p_{A}}[/tex]= Final momentum of piece A
[tex]\vec{p_{B}}[/tex]= Final momentum of piece B
The object is at rest before the explosion, then
[tex]0 = \vec{p_{A}}+\vec{p_{B}}[/tex]
[tex]\vec{p_{A}}=-\vec{p_{B}}[/tex]
The piece B is moving along positive x direction, then we have that
[tex]\vec{p_{B}} = 500kg\cdot m/s (\hat{i})[/tex]
Replacing,
[tex]\vec{p_{A}} = - 500kg\cdot m/s(\hat{i})[/tex]
The component of momentum in the part A is of [tex]500Kg \cdot m/s[/tex] in the negative direction of X.
