Game Development Reference
stability in your integration algorithms. We'll discuss these issues more when we show
you several simulation examples in Chapter 7 through Chapter 14 .
We've devoted this entire chapter to projectile motion because so many physical prob‐
lems that may find their way into your games fall in this category. Further, the forces
governing projectile motion affect many other systems that aren't necessarily projectiles
—for example, the drag force experienced by projectiles is similar to that experienced
by airplanes, cars, or any other object moving through a fluid such as air or water.
A projectile is an object that is placed in motion by a force acting over a very short period
of time, which, as you know from Chapter 5 , is also called an impulse. After the projectile
is set in motion by the initial impulse during the launching phase, the projectile enters
into the projectile motion phase, where there is no longer a thrust or propulsive force
acting on it. As you know already from the examples presented in Chapter 2 and Chap‐
ter 4 , there are other forces that act on projectiles. (For the moment, we're not talking
about self-propelled “projectiles” such as rockets since, due to their propulsive force,
they don't follow “classical” projectile motion until after they've expended their fuel.)
In the simplest case, neglecting aerodynamic effects, the only force acting on a projectile
other than the initial impulsive force is gravitation. For situations where the projectile
is near the earth's surface, the problem reduces to a constant acceleration problem.
Assuming that the earth's surface is flat—that is, that its curvature is large compared to
the range of the projectile—the following statements describe projectile motion:
• The trajectory is parabolic.
• The maximum range, for a given launch velocity, occurs when the launch angle is
• The velocity at impact is equal to the launch velocity when the launch point and
impact point are at the same level.
• The vertical component of velocity is 0 at the apex of the trajectory.
• The time required to reach the apex is equal to the time required to descend from
the apex to the point of impact assuming that the launch point and impact point
are at the same level.
• The time required to descend from the apex to the point of impact equals the time
required for an object to fall the same vertical distance when dropped straight down
from a height equal to the height of the apex.
There are four simple classes of projectile motion problems that we'll summarize:
• When the target and launch point are at the same level