Suppose a fireworks shell explodes, breaking into three large pieces for which air resistance is negligible. how is the motion of the center of mass affected by the explosion? how would it be affected if the pieces experienced significantly more air resistance than the intact shell?

Explanation:

                The term "center of the mass" of a system can be defined as the point on the system where the mass of the system is said to be concentrated. It is useful for linear  or rotational motion.

                Since the external force, since there is no air resistance, on the firework shell is zero, so the center of mass of the system will not move, it will remain at the same place.

                When the fire work shell explodes, it means that it has a proper inelastic collision. Here the momentum will be conserved and not the kinetic energy.

                 Now if there is more air resistance force, there is an external force acting on the mass and therefore the center of mass will now shift.

dude you should crop your image so only the question shows. but   can you explain it better

a factory opens that mass-produces light bulbs.

explanation:

not sure if that's an answer to your questions but this is an example! : )