When the ball is hit by the bat, the
bat exchanges its momentum to the ball and the ball flies away.
While the ball flies, both gravity and air will exert a force on
the ball, with gravity pulling the ball downward. Here are all the
forces that are effecting the ball:
http://library.thinkquest.org/11902/physics/range.html
In knowing what the parabolic equations for motion
are you can in general determine how far a ball will travel, and
how long it will take to get to that point. The equation you could
use would be:
x = 2(Vxi)*(Vyi) / g
Where x is the final position, Vxi is the initial
horizontal velocity, Vyi is the initial vertical velocity, and g
is the force of gravity which is normally 9.8 m/s/s.
t = x / Vxi
Where t is the time when, x is the current position,
and Vxi is the initial horizontal velocity.
The above equations work very well
in ideal situations mainly without air. The air causes a friction
on the ball called the drag force. Which is represented by
Fd = (Cd)(p)(Av)^2
Where Fd is the drag force, Cd is the drag coefficient,
p is the density of the air, A is the surface area of the object,
and v is the velocity of the object.