The question is incomplete. The mass of the object is 10 gram and travelling at a speed of 2 m/s.
Solution:
It is given that mass of object before explosion is,m = 10 g
Speed of object before explosion, v = 2 m/s
Let [tex]$m_1, m_2 \text{ and}\ m_3$[/tex] be the masses of the three fragments.
Let [tex]$v_1, v_2 \text{ and}\ v_3$[/tex] be the velocities of the three fragments.
Therefore, according to the law of conservation of momentum,
[tex]$mv=m_1v_1 +m_2v_2+m_3v_3$[/tex]
[tex]$10 \times 2 \hat i=3 \times 12 \hat{j} + 3(v_{2x} \hat{i}+v_{2y} \hat{j})-4 \times 9 \hat{j}$[/tex]
So the x- component of the velocity of the m2 fragment after the explosion is,
[tex]$3v_{2x} = 20$[/tex]
∴ [tex]$v_{2x} = 6.67 \ m/s$[/tex]
