HOMEWORK 03
Solutions
(1) Suggested Problems
(2) Suggested Problems
(3) Calvin the ant has recently found some spilled beer on a college campus. The
location of the spill is (1
,
2
,
0). He wishes to return to his anthill to report
on the Fnd, however, for some reason, he Fnds that instead of walking in a
straight path, he returns home along a path that has velocity
v
(
t
)=(cos
t
+1)
i
+5
j
+0
k
starting at time
t
=0
.
(a) What is Calvin’s actual path
r
(
t
)?
r
(
t
)=
°
v
(
t
)
dt
=(s
in
t
+
t
+
c
1
)
i
+(5
t
+
c
2
)
j
+
c
3
k
.T
os
o
l
v
ef
o
r
c
1
,c
2
,
and
c
3
we use his postion at
t
=0
.
r
(0) =
c
1
i
+
c
2
j
+
c
3
k
=
i
+2
j
+0
k
→
r
(
t
)=(s
in
t
+
t
+1)
i
+(5
t
+2)
j
+0
k
(b) If the entrance to the anthill is at (
3
π
2
,
15
π
+4
2
,
0), will Calvin make it to
the entrance? If so, when?
To make it to the entrance, there must be some value
t
0
for which
r
(
t
0
)=
3
π
2
i
+
15
π
+4
2
j
+0
k
.Th
i
sg
iv
e
su
sth
re
eequa
t
ion
s
:
sin
t
0
+
t
0
+1 =
3
π
2
5
t
0
+2 =
15
π
+4
2
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 ADAMNORRIS
 Arc Length, Derivative, Cos, The Entrance, New South Wales, Windows games, Kate

Click to edit the document details