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Mathematics
Problem
A journey consists of three consecutive segments described below. Segment A (
0
≤
t
≤
1
0 \le t \le 1
0
≤
t
≤
1
):
x
=
3
t
x = 3t
x
=
3
t
,
y
=
0
y = 0
y
=
0
Segment B (
1
≤
t
≤
2
1 \le t \le 2
1
≤
t
≤
2
):
x
=
3
+
3
cos
(
π
(
t
−
1
)
)
x = 3 + 3\cos\bigl(\pi (t-1)\bigr)
x
=
3
+
3
cos
(
π
(
t
−
1
)
)
,
y
=
3
sin
(
π
(
t
−
1
)
)
y = 3\sin\bigl(\pi (t-1)\bigr)
y
=
3
sin
(
π
(
t
−
1
)
)
Segment C (
2
≤
t
≤
3
2 \le t \le 3
2
≤
t
≤
3
):
x
=
3
−
3
(
t
−
2
)
x = 3 - 3(t-2)
x
=
3
−
3
(
t
−
2
)
,
y
=
0
y = 0
y
=
0
Determine the length of Segment B only.
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