Question

If a bomb at rest explodes into two pieces, the pieces must travel in opposite directions. Explain

Answer 1

A bomb at rest explodes into two pieces. Let the mass of bomb be $M$ and mass of two pieces be $m_1$ and $m_2$ respectively. Now, according to conservation of momentum:
$Mv=m_1{v}_1+M_2{v}_2$
Here $v=0$ (bomb is at rest) and $v_1$ and $v_2$ are velocities of two masses after explosion.
$M\left(0\right)=m_1{v}_1+m_2{v}_2$
$m_1{v}_1+m_2{v}_2=0$
$m_1{v}_1=-m_2{v}_2$
Now, masses cannot be negative that means the sign belongs to velocities. Therefore, the two pieces travel in opposite direction.