Game Development Reference

In-Depth Information

• When the target is at a level higher than the launch point

• When the target is at a level lower than the launch point

• When the projectile is dropped from a moving system (like an airplane) above the

target

In the first type of problem, the launch point and the target point are located on the

same horizontal plane. In
Figure 6-1
,
v
0
is the initial velocity of the projectile at the time

of launch, φ is the launch angle,
R
is the range of the projectile, and
h
is the height of

the apex of the trajectory.

Figure 6-1. Target and launch point at same level

To solve this type of problem, use the formulas shown in
Table 6-1
. Note, in these

formulas
t
represents any time instant after launch, and
T
represents the total time from

launch to impact.

Table 6-1. Formulas—target and launch point at same level

To calculate:

Use this formula:

x(t)

(v
o
cos φ) t

y(t)

(v
o
sin φ) t - (g t
2
) / 2

v
x
(t)

v
o
cos φ

v
y
(t)

v
o
sin φ - g t

v(t)

v
0
2

- 2
gtv
0
sin
φ
+
g
2
t
2

h

(v
o
2
sin
2
φ) / (2 g)

R

v
o
T cos φ

T

(2 v
o
sin φ) / g

Remember to keep your units consistent when applying these formulas. If you are

working in the SI (metric) system, length and distance values should be in meters (m);