You've read that the net force acting on an systems will change the system's momentum, but until now you haven't considered any particular forces. The first force that you will consider is the one that results from the interaction between objects with mass: the gravitational force.

For now, you will consider only the motion of systems near the surface of the Earth. Near the surface of the Earth, we observe that the gravitational force is a constant vector.¹⁾ Later, you will find that the gravitational force near the surface of the Earth is an approximation to the more general description of the gravitational force between objects.

Countless experiments near the surface of the Earth have shown that the force that the Earth exerts on a system with mass is the product of the system's mass ($m$) and the local gravitational acceleration ($\vec{g}$). Mathematically, we represent this force like this:

$$\vec{F}_{Earth} = m\vec{g}$$

where the local gravitational acceleration is directed towards the center of the Earth. In your typical “flat-Earth” models,²⁾ you will say the gravitational acceleration points “downward”, which we typically consider to be the negative $y$-direction. In this case,

$$\vec{g} = \langle 0, -g, 0\rangle \approx \langle 0, -9.81, 0\rangle \dfrac{m}{s}$$

where we have defined “up” as positive $y$-direction and the magnitude of the gravitational acceleration ($g$) is equal to 9.81 $\dfrac{m}{s}$. We also accept some variation in $\vec{g}$ from place to place.

The figure on the right represents a typical force body diagram for two systems falling near the surface of the Earth (where we have neglected any interactions due to the air). Notice that while the two systems experience different forces, they experience the same acceleration.

As you have read, the motion of a system depends on the net force acting on that system. If you can reasonably assume that a system interacts solely with the Earth such that the only force acting on that system is the local gravitational force, then the net force on that system is just the gravitational force. The motion of such a system is independent of the mass of the system.

The momentum of the system changes through the momentum principle, but the motion (how the position of the system changes) only depends on how the velocity changes. When the system only interacts with the Earth, this velocity change only depends on the gravitational acceleration. This can be summarized mathematically like this:

$$\Delta \vec{p} = \vec{F}_{net} \Delta t = \vec{F}_{Earth} \Delta t = m\vec{g}\Delta t$$ $$\Delta \vec{v} = \dfrac{\Delta \vec{p}}{m} = \dfrac{\vec{F}_{Earth}}{m} \Delta t = \vec{g}\Delta t$$

These algebraic manipulations produce a single “kinematic” equation that can be used to predict the future velocity of the system ($\vec{v}_f$) after some time ($\Delta t$) given information about its current velocity ($\vec{v}_i$).

$$\vec{v}_f = \vec{v}_i + \vec{g}\Delta t$$

which in component form is