A warm basball would travel further since the molecules in the ball are moving faster than if it was colder. Although this change of temperature would be very insignificant in everyday life. There would be a greeter affect in the distance if the bat was warm compared to the ball being warm. So if you wan't the ball to travel far have a warm bat and then it will have a lot of 'pop'. If you hit it with a bat, a warm ball will go further. The molecules in the ball are held together less tightly and are more bouncy, so instead of work being done by vibrating the bat, all energy is transferred into the ball.
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Yes. If a ball is hit with the same force in the same direction when it is hot, it will travel farther than if it was hit when it was cold out. This is because the density of the air. When it is hot out the density of the air is less than when it is cold it is better.
That is the sort of question that could be easily tested by actual experiment. In theory yes, a cold baseball might travel very slightly farther than a warm one, because the cold would make it contract (very slightly) and therefore it would present a smaller surface area to the air, producing less air resistance. I'm not sure that this effect would be large enough to actually detect, however.
I think a cold dry baseball would travel farther. A warm moist one would be heavier.
I would say maybe a little bit,the leather in the new ball will have more moisture than an old crusty one,so it might,in theory, get more of a bounce and go a little farther....