Projectiles

A Cannon Firing a Projectile — **Fig. 1 - A Projectile Fired From a Cannon**

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

Abbreviations

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

Notations

Abbreviation	Meaning
u	Initial velocity
v	Final velocity
a	Acceleration
t	Time
s	Distance

Equations

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 * t ², another useful equation of motion