APPM 2350
EXAM 1
FALL 2010
INSTRUCTIONS:
Electronic devices are not permitted during the exam. Write your name, your instructor’s
name, and your recitation number on the front of your bluebook. Start each problem on a new righthand page.
Justify your work clearly and
box
your Fnal answer. A correct answer with incorrect or no supporting work may
receive no credit, while an incorrect answer with relevant work may receive partial credit.
1. (25 points) Consider a particle moving along a path
r
(
t
) such that its speed is always
√
37, the curvature is
always 1
/
37, the acceleration is
a
(
t
)=
−
cos(
t
)
i
+0
j
−
sin(
t
)
k
, and the unit tangent to the path is
T
(
t
)=
(1
/
√
37)(
−
sin(
t
)
i
+6
j
+ cos(
t
)
k
).
(a) Calculate the velocity,
V
(
t
).
(b) Calculate the unit normal to the path,
N
(
t
).
(c) Calculate the unit binormal to the path,
B
(
t
).
(d) At time
t
°
=2
π
the particle is located at (1
,
12
π,
0). Determine
r
(
t
).
(e) Determine the constants
a
,
b
, and
c
, if one were to write the position vector at time
t
°
in the form
r
(
t
°
)=
a
T
(
t
°
)+
b
N
(
t
°
)+
c
B
(
t
°
).
2. (25 points) Suppose a probe is launched into deep space at time
t
= 0 from its mother ship to search for other
lifeforms that understand vector calculus. The probe travels along with velocity
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 Fall '07
 ADAMNORRIS
 Mother Ship

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