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With consistent force being the same using both bat's, it would be a linear equation essentially. Even so, if the only difference is the length, or leverage, it doesn't matter at all. A 45" bat will hit the ball the same distance as a 48" bat if collision was to occur in the exact middle. The only difference would be the mass, mass only makes use of itself in a forceful way if it can all be utilized. It cannot all be utilized if you hit it in the center, it has to be at the farthest end from the handle to be utilized. It's like lighting a 60 second fuse on a stick of dynamite half-way down and still expecting the full seconds of safety...... not gonna happen.

Now, if you were a good batter and utilized the 47th inch of the 48 inch bat, you could gain at least 20 ft with the bat moving @ about 75 mph as oppose the 44th inch of the 45 inch bat @ 75 mph. It's the weight that matters though, not necessarily the length.

force x mass = accel

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Q: How much farther will a 48 inch shaft on a driver hit a ball than a 45 inch assuming center hits?
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