Physics Question on work, energy and power

Question

A projectile of mass $M$ is fired so that the horizontal range is $4\, km$ . At the highest point the projectile explodes in two parts of masses $M/4$ and $3M/4$ respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is :

Answer 1

Solution

The correct option is(C): 10 km

$X _{ COM }=\frac{ m _{1} x _{1}+ m _{2} x _{2}}{ m _{1}+ m _{2}}$
$R =\frac{\frac{ M }{4} x +\frac{3 M }{4} \times \frac{ R }{2}}{ M }$

Horizontal range is given as
$r_{\frac{M}{4}}=\frac{r}{2}+d=2+8=10km$
$=10 Km$