A projectile is shot with an initial speed of $50\,\frac{m}{s}$ with an angle of $53^{\circ}$. On its highest point of its trajectory it explodes splitting in two fragments of the same mass, one of them inmediately after the collision has zero in speed and fells vertically. Find the horizontal distance in $m$ which the other fragment travels. You may use $g=10\,\frac{m}{s^2}$.

The alternatives are as follows:

$\begin{array}{ll}

1.&120\,m\\

2.&180\,m\\

3.&200\,m\\

4.&240\,m\\

5.&320\,m\\

\end{array}$

I'm not sure how to tackle this problem. I am assuming that it has to do with the conservation of momentum but I don't know how should I proceed with an explosion.

The only thing which I can say is that the components of the bullet will be:

$v_x=50\cos53^{\circ}= 50\times\frac{3}{5}=30$

$v_y=50\sin53^{\circ}= 50 \times \frac{4}{5}=40$

And i believe that these speeds might be used in the analysis for the explosion but I'm not sure what to do with those, am I right with my analysis?. Can someone help me with this thing please?.