Game Development Reference
In-Depth Information
This is equivalent to the solution
()
(
)
x t
=
D βt δ
sin
+
,
where
2
2
D
=
CC
C
+
1
2
1
1
δ
=
sin
.
D
Projectile Motion
The position
()
x
t
of a projectile is given by the function
()
x
t
=+ +
x
v
t
g
t
2
1
,
0
0
2
where
g is the
acceleration of gravity. The maximum height h attained by the projectile is given
by
x is the initial position,
v is the initial velocity, and
=
0, 0,
g
2
v
z
hz
=+
,
0
2
g
and the range r of the projectile is given by
2 x
vv
z
r
=
.
g
Resisted Motion
The position function
()
x
t
for an object moving through a resistive medium is
given by
g
k
v
g
(
)
()
0
kt
x
t
=++
x
t
1
e
,
0
k
k
2
where k represents the intensity of the damping force. The terminal velocity
v is
given by
g
v
=
.
T
k
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