"Newton's Second Law states that the change of motion is proportional to the motive power impressed and is made in the direction of the right line in which that force is impressed"

Forces acting on a paintball in motion are mainly:
Gravity
Drag Forces

Forces affecting trajectory:
While the paintball is in flight a main force that affect trajectory is the Magnus Effect.


Image taken from http://lennon.csufresno.edu/~nas31/nsa/pballIntro1.html

The Magnus Effect:
    An important force often overlooked when analyzing a spinning projectile, the Magnus Effect (also referred to as the Robbins effect) is when
    a "rapidly spinning ball develops another force at right angles to the spin axis," This force often causes what's known as a lift force, allowing
    the ball to continue it's flight path and possibly gain trajectory, giving it a farther distance.

As seen from the above diagram, you can see the flow lines of air on the ball as it travels through the air. The air on top is flowing faster than the air on the bottom of the ball,
causing a spinning effect due to the "net change in air pressure between the top and the bottom of the ball,". With this specific case the ball would have a force upward.
With an opposite example, the ball would have spun downward.

On to Velocity

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