The problem is complicated, so lets simplify and then look at two limiting cases and see what they suggest.
First, it is simpler to ask which ball leaves the bat in a “forward” direction faster. Presumably the one that leaves faster also goes further. The collision is “elastic” neither the bat nor the ball gets permananetly crushed in a way as to take energy out of the system.
The two limiting cases to look at
1) bat is moving at 0 velocit and weighs same as ball
Then either the 60 or the 90 mph ball come to a dead stop on contact with the bat and the bat recedes at 60 or 90 mph backwards.
2) the bat is moving at 0 velocity and weighs a tremendous amount more than the ball. Then the (60, 90) mph ball hitting the very heavy stationary “bat” bounce off it in the forward direction at (60, 90) mph and the bat remains essentially stationary.
So we see for bats between the weight of the ball and infinity (and I think this is the true range of bat weights), the 60 mph ball never goes faster than the 90 mph ball, but sometimes the 90 mph ball goes faster. I think details of how fast the bat is actually going will not matter, that we have surrounded the problem with this simplification, and the fast ball goes further when hit well.
The problem is complicated, so lets simplify and then look at two limiting cases and see what they suggest.
First, it is simpler to ask which ball leaves the bat in a “forward” direction faster. Presumably the one that leaves faster also goes further. The collision is “elastic” neither the bat nor the ball gets permananetly crushed in a way as to take energy out of the system.
The two limiting cases to look at 1) bat is moving at 0 velocit and weighs same as ball Then either the 60 or the 90 mph ball come to a dead stop on contact with the bat and the bat recedes at 60 or 90 mph backwards. 2) the bat is moving at 0 velocity and weighs a tremendous amount more than the ball. Then the (60, 90) mph ball hitting the very heavy stationary “bat” bounce off it in the forward direction at (60, 90) mph and the bat remains essentially stationary.
So we see for bats between the weight of the ball and infinity (and I think this is the true range of bat weights), the 60 mph ball never goes faster than the 90 mph ball, but sometimes the 90 mph ball goes faster. I think details of how fast the bat is actually going will not matter, that we have surrounded the problem with this simplification, and the fast ball goes further when hit well.