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Mathematics
408
K: Homework
8
Gagan Tara Nanda
09
th
October,
2004
HW
8
:
#
s
8
,
10
,
12
,
20
,
21
,
22
8. I’ve clipped the diagram below from the original solutions, so to have it match my question, change the
length
5
in the diagram to
8
,s
incetheis
landinmyquest
ionis
8
miles from the shore.
In this setup,
x
isthed
istanceofthel
ightbeam
’sendpo
intfromtheleftedgeoftheshorel
ine
.Wewant
to know how fast the beam is travelling along the shore line, so we want to
f
nd
dx
dt
. From the diagram,
tan
θ
=
x
8
⇒
x
=8tan
θ
.
Di
f
erentiate implicitly with respect to
t
to get
dx
dt
=8sec
2
d
θ
dt
.
Observe that
1
revolution is
2
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View Full DocumentGagan Tara Nanda
2
which is
d
θ
dt
. Hence
dx
dt
=8
s
e
c
2
θ
(8
π
)
=
64
π
cos
2
θ
.
At the particular instant requested, the beam makes an angle of
45
◦
with the shoreline, which is
90
◦
−
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