Game Development Reference
InDepth Information
The horizontal distance that a projectile travels before returning to the height
from which it was launched is called the projectile's range. If a projectile is
launched from a horizontal plane at
0
z
=
0
, then the time
t
at which it lands is
given by the solution to the equation
2
v t
−
1
2
t
=
0
.
(13.80)
One solution to this equation is
, corresponding to the time when the projec
tile was launched. The other solution is
=
t
0
2
z
v
t
=
,
(13.81)
g
and as we would expect, this is twice as long as it takes for the projectile to reach
its maximum height. If we assume that the projectile follows a path lying in the
x

z
plane, then plugging this time into the function
()
x t
and subtracting the initial
x
coordinate
x
gives us the following expression for the range
r
of a projectile.
2
x
vv
z
r
=
(13.82)
g
Example 13.8.
A projectile is launched with an initial speed of 30m s in a di
rection forming an angle of 40 degrees with the ground (see Figure 13.3). As
suming the ground is flat down range, how far does the projectile travel before
landing?
v
0
40
°
Figure 13.3.
The projectile used in Example 13.8.
Solution.
We assume that the projectile is launched from the origin and that the
path of the projectile lies in the
x

z
plane. The
v
and
v
components of the initial
velocity are given by
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