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  4. 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 :

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Q. 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 :

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Solution:

$X _{ COM }=\frac{ m _{1} x _{1}+ m _{2} x _{2}}{ m _{1}+ m _{2}}$
$R =\frac{\frac{ M }{4} x +\frac{3 M }{4} \times \frac{ R }{2}}{ M }$
$\Rightarrow x =10 Km$