Graphics Reference
In-Depth Information
Note that if you are located at the origin, t
C
becomes
t
C
=
−ˆ
v
O
·
q
(11.7)
s
O
and
d
becomes
d
=
q
+
t
C
s
O
ˆ
v
O
(11.8)
For example, say you are located at the origin and the object is located at Q, 120 km along the
x-axis, as shown in Fig. 11.3.
Y
C
d
Y
ou
v
o
Q
q
120
X
Z
Figure 11.3.
60
kmh
−
1
in the direction
1
√
3
If the object's speed is s
O
=
v
O
=
ˆ
−
i
+
j
+
k
, the time to reach
C is given by
1
√
3
−
−
i
+
j
+
k
·
120
i
3
√
3
2
√
3
=
2
t
C
=
=
60
t
C
=
1155 h
The shortest distance
d
is given by
k
3
√
3
2
1
√
3
d
=
q
+
t
C
s
O
ˆ
v
O
=
120i
+
×
60
×
−
i
+
j
+
d
=
120
i
−
40
i
+
40
j
+
40
k
=
80
i
+
40
j
+
40
k
40
√
6
d
=
40
2
i
+
j
+
k
=
98 km
11.3 Close encounters of the second kind
The next problem is to consider the scenario when both you and the object are moving! Well,
the secret is to translate the problem from one of absolute values to that of relative values. For
example, if you are defined as follows:
location:
y
,
velocity: s
Y
ˆ
v
Y
,
