They work together to do it. Both objects experience the same force (Newton’s third law) during the collision. But we could determine which one brings more energy to the event.
A baseball is 0.15kg and is going 40 m/s. That’s 120 joules of kinetic energy.
The bat is much larger at 1 kg. It’s traveling roughly 30 m/s. That brings about 450 j of energy.
So the bat contributes the majority of the energy and an argument could be made that it is the more significant “cause”
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