find b as a function of v (b(v)) as explaind in task (i)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Hey! Just got this answer, thanks! But I still need to find b as a function of v (b(v)) as explaind in task (i)
Transcribed Image Text:19:05 P
Answered: Donald play...
bartleby.com
= bartleby
Q
E Q&A
Math / Advanced M... / Q&A Libr... / Donald plays monop...
Donald plays monopoly and get "go dire...
Donald plays monopoly and get "go direct to
prison". He wants to go to the prison as fast as
possible, but discovers there is a swamp between
him and the prison. Donald is in the point (2, 0)
and the prison (-2, 0), and the swamp inside the
curve Ixl + lyl = 1. Donald moves with a speed 1
outside the swamp, and constant speed v>0 in
the swamp.
What can the speed in the swamp be if:
(i) The fastest way involves to start by going
straight forward to a point (a, b) at the edge of the
swamp with 0 < Ibl < 1(se picture) if so , fin b as a
function of v and draw the graph.
(ii) the fastest way is to go outside the swamp (b=
+- 1)?
(iii) The fastest way is to go straight through the
swamp (b= 0)?
The task: Explain that the picture shows donalds
path in case (i) and the time he uses can be given
as a function of b
t(b) = 2 *V(1+2b+2b²) +2 *((1-b)/v)
SwAMB
PRISON
Transcribed Image Text:19:05 E
= bartleby
E Q&A A e
Math Advanced M... /Q&A Libr... /Donald plays monop.
Donald plays monopoly and get "go dire...
Solution:
Donald plays monopoly and get "go direct to
prison". He wants to go to the prison as fast as
possible, but discovers there is a swamp between
him and the prison. Donald is in the point (2, 0)
and the prisun 2, 0), and the swamp inside the
curve Ixl + lyl = 1. Donald moves witha speed 1
outside the swamp, and constant speed v-0 in
the swarmp.
What can be the speed in the swamp be if:
li) The fastest way involves to start by going
straight forward to a point (a, b) at the edge of the
sawamp with D< Ibl < 1(see picture) if so , fin b as a
function of v and draw the graph.
The distance covered outside the swamp from (2,
0) to (a, b) is d = V + (a – 2
As Donald moves with a speed 1 outside the
swamp, the time taken becomes
2 = = Vi + (a - 2)
The distance covered inside the swamp from (a,
bị to (-a, bị is d = vo' + (-a - a) = 20 .
As Donald moves with constant speed v-0 in the
swamp, the time taken becomes 12 = - .
Further we have
The distarnce covered outside the swamp frorm (-
a, b) to ( 2,0) is di = v + (a – 2)
As Donald moves with a speed 1 outside the
swamp, the time taken becomes
= = Vi + (a - 2
Total time taken:
i=1 + +i
=V + (a - 2 ++ v + le - 27
=v +(1 - 5 - 2y + - + V+ (1 -- 2)
21-
+ V + (1 - - 2)2
21-
=2V1 + 2 + 26 + -
As the distance in the swamp covered is
d; = 2(1- b) , the speed when 0< |b| < 1 becormes
Obtain the time and speed in the swamp:
When b-0: =2y1 + 2(0) +2 (0) + AS = 2+
The speed whenb=0 becomes
-.
When b-1: =2v1 + 2(1) + 20) + " - zy5
The speed whenb-1 becomes - 0.
When b=-1:
1=2y1+ 21-1)" + 2(-1) + 2 = 2 +
21-:-1
The speed whenb=1 becomes
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