(a) Consider a boat in the ocean, which is carrying contraband. Near to this boat is a lighthouse on a small island, which is attempting to track this boat with its searchlight. This ray of light originates at the lighthouse, and passes through the boat's position precisely at all times. The boat tries to escape the lighthouses' tracking by moving at a constant angle relative to the ray of light. i. Write a differential equation which models the boat's path through the ocean. You ㅠ 3π may assume that 0 or for convenience's sake. " 2 Hint: It may be helpful to consider the angle a(t) between the lighthouse and the boat at time t, as well as fixing the lighthouse as the origin. ㅠ ii. Suppose 4' kilometres to the north of the lighthouse. Solve for the trajectory of the boat. Write your answer in polar coordinates. = and is first discovered at the position 3 kilometres east, and 4 a) het x (t) and yet) be olan the boat moves. tan & dx dt at ray of light; dano Differentiating seca x lighthouse and da ste dt da 0 (x) (6) Алекрон ۶ (۰) at time t. het 2 (t) be boat dt Msing chain terms of substituling duy fue dx = = 5 > = сол Ө dy y र्गेहै the x do arc dx the d x dt dt 2 = (casa) x (de dat • tano) (case) rule tano and at ting constant angle tan l (2) de aut dy dt the position of the the ни dy at wir.t. 't'. - (*) and simplilying, x/do dt boat is discovered at position (2,4) in km. and 0 (0) tan (7) The solution in polar wordinates is M(+)=5 = sin o tano arc dx dt can express dx and dt 4 + 3 tan (4) 3 y tan (1) angle between 't'. since the relative to + ше 114 boat in the get. dy in at x exp(-t)
(a) Consider a boat in the ocean, which is carrying contraband. Near to this boat is a lighthouse on a small island, which is attempting to track this boat with its searchlight. This ray of light originates at the lighthouse, and passes through the boat's position precisely at all times. The boat tries to escape the lighthouses' tracking by moving at a constant angle relative to the ray of light. i. Write a differential equation which models the boat's path through the ocean. You ㅠ 3π may assume that 0 or for convenience's sake. " 2 Hint: It may be helpful to consider the angle a(t) between the lighthouse and the boat at time t, as well as fixing the lighthouse as the origin. ㅠ ii. Suppose 4' kilometres to the north of the lighthouse. Solve for the trajectory of the boat. Write your answer in polar coordinates. = and is first discovered at the position 3 kilometres east, and 4 a) het x (t) and yet) be olan the boat moves. tan & dx dt at ray of light; dano Differentiating seca x lighthouse and da ste dt da 0 (x) (6) Алекрон ۶ (۰) at time t. het 2 (t) be boat dt Msing chain terms of substituling duy fue dx = = 5 > = сол Ө dy y र्गेहै the x do arc dx the d x dt dt 2 = (casa) x (de dat • tano) (case) rule tano and at ting constant angle tan l (2) de aut dy dt the position of the the ни dy at wir.t. 't'. - (*) and simplilying, x/do dt boat is discovered at position (2,4) in km. and 0 (0) tan (7) The solution in polar wordinates is M(+)=5 = sin o tano arc dx dt can express dx and dt 4 + 3 tan (4) 3 y tan (1) angle between 't'. since the relative to + ше 114 boat in the get. dy in at x exp(-t)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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can somebody do out the chain rule and show me how to simplify it to get the equation please. the question is also attached. it can be found at this link ~ https://www.bartleby.com/questions-and-answers/1.-consider-a-boat-in-the-ocean-which-is-carrying-contraband.-near-to-this-boat-is-a-lighthouse-on-a/def1c091-4dfa-46b8-98cf-2bb871128d4e
Transcribed Image Text:(a) Consider a boat in the ocean, which is carrying contraband. Near to this boat is a
lighthouse on a small island, which is attempting to track this boat with its searchlight.
This ray of light originates at the lighthouse, and passes through the boat's position
precisely at all times. The boat tries to escape the lighthouses' tracking by moving at a
constant angle relative to the ray of light.
i. Write a differential equation which models the boat's path through the ocean. You
ㅠ 3π
may assume that 0
or for convenience's sake.
"
2
Hint: It may be helpful to consider the angle a(t) between the lighthouse and the boat
at time t, as well as fixing the lighthouse as the origin.
ㅠ
ii. Suppose
4'
kilometres to the north of the lighthouse.
Solve for the trajectory of the boat. Write your answer in polar coordinates.
=
and is first discovered at the position 3 kilometres east, and 4
Transcribed Image Text:a) het x (t) and yet) be
olan
the
boat moves.
tan &
dx
dt
at
ray of light;
dano
Differentiating
seca x
lighthouse and
da ste
dt
da
0 (x)
(6) Алекрон
۶ (۰)
at time t. het 2 (t) be
boat
dt
Msing chain
terms of
substituling duy fue
dx
=
= 5
>
=
сол Ө
dy
y
र्गेहै
the
x
do
arc
dx
the
d x
dt
dt
2
= (casa) x (de dat • tano)
(case)
rule
tano
and
at ting
constant angle
tan l
(2) de aut
dy
dt
the position of the
the
ни
dy
at
wir.t. 't'.
-
(*)
and simplilying,
x/do
dt
boat is discovered at position (2,4) in km.
and 0 (0)
tan
(7)
The solution in polar wordinates is
M(+)=5
= sin o
tano
arc
dx
dt
can express dx and
dt
4 + 3 tan (4)
3
y tan (1)
angle between
't'. since the
relative to
+
ше
114
boat in the
get.
dy in
at
x exp(-t)
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