Asteroid Momentum & Starbase Alpha Impact

[iNCREDiBLE]

An asteroid is spotted moving directly toward the center of Starbase Alpha. The frightened residents fire a missile at the asteriod, which breaks it into two chunks, one with 2.4 times the mass of the other. The chunks both pass the starbase at the same time. If the lighter chunk passes 1800 m from one edge of the 2.2-km-wide starbase, will the other chunk hit or miss the starbase?My intuition says that I should do this:
The lighter chunk misses the center of the building with 1800+2200/2 = 2900 meters. The other part will land 2900/2.4 = 1208 meters away from the center of the building...?

 

[chaoseverlasting]

Apply the conservation of linear momentum.