To solve for the motion of the baseball, we can use the equations of motion that considers both the effect of air resistance and gravity. Let's break down the initial velocity of the baseball into its horizontal and vertical components:

V0x = V0 * cos(45°)
V0y = V0 * sin(45°)

where V0 is the initial velocity of the baseball.

The acceleration due to air resistance can be calculated using the following equation:

a_drag = (0.5 * ρ * C * A * v^2) / m

where ρ is the density of air, C is the drag coefficient, A is the cross-sectional area of the baseball, v is the instantaneous velocity of the baseball, and m is the mass of the baseball.

Since the baseball is hit at an angle of 45 degrees above the horizontal, the acceleration in the horizontal direction is zero, and in the vertical direction, the acceleration can be calculated as:

a_y = -g + a_drag

where g is the acceleration due to gravity.

To calculate the range of the baseball, we need to determine the time it takes for the ball to reach the ground. This can be found using the equation:

y = V0y * t + (1/2) * a_y * t^2

Since the ball reaches the ground when y = 0, we can solve for t:

0 = V0y * t + (1/2) * a_y * t^2

Using the quadratic formula:

t = [-V0y ± sqrt(V0y^2 - 2 * a_y * 0)] / a_y

We discard the negative root because time cannot be negative.

Once we have the time of flight, we can calculate the range using the equation:

R = V0x * t

Finally, to account for air resistance, the initial velocity (V0) would need to be calculated (by trial and error) to satisfy the range obtained with the given drag coefficient.

Please note that the above calculations are theoretical and may not exactly correspond to the actual motion of a baseball due to factors such as wind, seam orientation, spin, and so on.

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