Answer:
[tex]v_2=-133.17m/s[/tex], the minus meaning west.
Explanation:
We know that linear momentum must be conserved, so it will be the same before ([tex]p_i[/tex]) and after ([tex]p_f[/tex]) the explosion. We will take the east direction as positive.
Before the explosion we have [tex]p_i=m_iv_i=Mv_i[/tex].
After the explosion we have pieces 1 and 2, so [tex]p_f=m_1v_1+m_2v_2[/tex].
These equations must be vectorial but since we look at the instants before and after the explosions and the bomb fragments in only 2 pieces the problem can be simplified in one dimension with direction east-west.
Since we know momentum must be conserved we have:
[tex]Mv_i=m_1v_1+m_2v_2[/tex]
Which means (since we want [tex]v_2[/tex] and [tex]M=m_1+m_2[/tex]):
[tex]v_2=\frac{Mv_i-m_1v_1}{m_2}=\frac{Mv_i-m_1v_1}{M-m_1}[/tex]
So for our values we have:
[tex]v_2=\frac{(145kg)(24m/s)-(115kg)(65m/s)}{(145kg-115kg)}=-133.17m/s[/tex]
