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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