Projectiles

In 1600s, armies used equations of motions to calculate velocities and angle for firing a missile to hit a target. While a quarterback does not do explicit calculations using equations of motion, a computerized football game will certainly need to do these calculations.
We will use the metric notations that are favored for all scientific and engineering calculations

The following abbreviations will be used:

meters, m
kilometers, km: 1000 meters make up a kilometer
meters per second, m/s: units for measuring distance
meters per second squared, m/s ²: units for measuring acceleration

The following physics notation will be used:

Initial velocity, u
Final velocity, v
Acceleration, a
Time, t
Distance, s

Therefore, some of the useful equations of motion for us are:

a = (v - u) / t, which can be arranged to get the following equation
t = (v - u) / a, which can be further arranged as
v = u + a * t
s = u * t + 0.5 * a * t² , another useful equation of motion