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Mathematics
Mathematics
Problem
A projectile is launched at time
t
=
0
t=0
t
=
0
, and its velocity for
t
≥
0
t\ge 0
t
≥
0
is
v
(
t
)
=
⟨
4
cos
t
,
4
sin
t
,
t
⟩
\mathbf v(t)=\langle 4\cos t,\,4\sin t,\,t\rangle
v
(
t
)
=
⟨
4
cos
t
,
4
sin
t
,
t
⟩
. At time
t
=
π
t=\pi
t
=
π
, its position is
r
(
π
)
=
⟨
6
,
−
2
,
7
⟩
\mathbf r(\pi)=\langle 6,\,-2,\,7\rangle
r
(
π
)
=
⟨
6
,
−
2
,
7
⟩
. What is
r
(
2
π
)
\mathbf r(2\pi)
r
(
2
π
)
? a)
⟨
6
,
6
,
3
π
2
2
+
7
⟩
\langle 6,6,\tfrac{3\pi^2}{2}+7\rangle
⟨
6
,
6
,
2
3
π
2
+
7
⟩
b)
⟨
6
,
−
10
,
3
π
2
2
+
7
⟩
\langle 6,-10,\tfrac{3\pi^2}{2}+7\rangle
⟨
6
,
−
10
,
2
3
π
2
+
7
⟩
c)
⟨
6
,
−
10
,
3
π
2
+
7
⟩
\langle 6,-10,3\pi^2+7\rangle
⟨
6
,
−
10
,
3
π
2
+
7
⟩
d)
⟨
10
,
−
2
,
3
π
2
2
+
7
⟩
\langle 10,-2,\tfrac{3\pi^2}{2}+7\rangle
⟨
10
,
−
2
,
2
3
π
2
+
7
⟩
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