Projectile Motion of an Exploding Shell

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A 75 kg shell is fired with an initial speed of 125 m/s at an angle 55 degrees above horizontal. Air resistance is negligible. At its highest point, the shell explodes into two fragments, one four times more massive than the other. The heavier fragment lands directly below the point of the explosion. If the explosion exerts forces only in the horizontal direction, how far from the launch point does the lighter fragment land?

Alright so I know you have to find the projectile motion before the explosion. So you would divide it up into 125sin(55) and 125cos(55). Then you need to find where its highest point is or where the velocity is equal to zero. Then you take this point and the horizontal velocity and use 1/5 of the 75kg shell or 15kg. Then its just like a rolling object off a table right?
 
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At the highest point the velocity isn't zero, but one of the components is.
 
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