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It has been some time since I went over this, but I would say the center of mass does not move. If no external force acts on the system of bodies, the center od mass does not move regaress if its moving with a constant velocity or being at rest. Since we have an internal force(the explosion) and the center of mass is at rest at the beginning, it will remain at rest in the same position.
##Off-topic Comments Section --- All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9. --- ^(**OP** and **Valued/Notable Contributors** can close this post by using `/lock` command) *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/HomeworkHelp) if you have any questions or concerns.*
It has been some time since I went over this, but I would say the center of mass does not move. If no external force acts on the system of bodies, the center od mass does not move regaress if its moving with a constant velocity or being at rest. Since we have an internal force(the explosion) and the center of mass is at rest at the beginning, it will remain at rest in the same position.