A cable of 80 meters (m) is hanging from the top of two poles that are both 50 m from the ground. What is the...
$begingroup$
Hey guys I ran accross this problem while watching a YouTube video.
A cable of $80$ meters (m) is hanging from the top of two poles that are both $50$ m from the ground. What is the distance between the two poles, to one decimal place, if the center of the cable is:
(a) 20 m above the ground?
And yes, I did come across a solution involving hyperbolic trig but that's not what I am interested in.
I am interested in figuring out another way to solve this problem that does not involve using $sinh$. I am thinking that we can assume that this is a parabola because clearly there is a vertex there is symmetry. Is this assumption correct? Am I going to get anywhere with this assumption?
calculus algebra-precalculus trigonometry
asked Aug 21 '18 at 18:18
combo studentcombo student
567310
$endgroup$
add a comment |
$begingroup$
Hey guys I ran accross this problem while watching a YouTube video.
A cable of $80$ meters (m) is hanging from the top of two poles that are both $50$ m from the ground. What is the distance between the two poles, to one decimal place, if the center of the cable is:
(a) 20 m above the ground?
And yes, I did come across a solution involving hyperbolic trig but that's not what I am interested in.
I am interested in figuring out another way to solve this problem that does not involve using $sinh$. I am thinking that we can assume that this is a parabola because clearly there is a vertex there is symmetry. Is this assumption correct? Am I going to get anywhere with this assumption?
calculus algebra-precalculus trigonometry
asked Aug 21 '18 at 18:18
combo studentcombo student
567310
$endgroup$
$begingroup$
It's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:23
$begingroup$
how do you know?
$endgroup$
– combo student
Aug 21 '18 at 18:23
$begingroup$
Because it's well known what kind of curve a hanging cable will describe, and while I don't remember the name right now, I do remember that it's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:27
2
$begingroup$
It's called a catenary.
$endgroup$
– Robert Israel
Aug 21 '18 at 18:29
add a comment |
$begingroup$
Hey guys I ran accross this problem while watching a YouTube video.
A cable of $80$ meters (m) is hanging from the top of two poles that are both $50$ m from the ground. What is the distance between the two poles, to one decimal place, if the center of the cable is:
(a) 20 m above the ground?
And yes, I did come across a solution involving hyperbolic trig but that's not what I am interested in.
I am interested in figuring out another way to solve this problem that does not involve using $sinh$. I am thinking that we can assume that this is a parabola because clearly there is a vertex there is symmetry. Is this assumption correct? Am I going to get anywhere with this assumption?
calculus algebra-precalculus trigonometry
asked Aug 21 '18 at 18:18
combo studentcombo student
567310
$endgroup$
Hey guys I ran accross this problem while watching a YouTube video.
A cable of $80$ meters (m) is hanging from the top of two poles that are both $50$ m from the ground. What is the distance between the two poles, to one decimal place, if the center of the cable is:
(a) 20 m above the ground?
And yes, I did come across a solution involving hyperbolic trig but that's not what I am interested in.
I am interested in figuring out another way to solve this problem that does not involve using $sinh$. I am thinking that we can assume that this is a parabola because clearly there is a vertex there is symmetry. Is this assumption correct? Am I going to get anywhere with this assumption?
calculus algebra-precalculus trigonometry
calculus algebra-precalculus trigonometry
asked Aug 21 '18 at 18:18
combo studentcombo student
567310
asked Aug 21 '18 at 18:18
combo studentcombo student
567310
asked Aug 21 '18 at 18:18
combo studentcombo student
567310
asked Aug 21 '18 at 18:18
combo studentcombo student
567310
asked Aug 21 '18 at 18:18
combo studentcombo student
567310
567310
$begingroup$
It's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:23
$begingroup$
how do you know?
$endgroup$
– combo student
Aug 21 '18 at 18:23
$begingroup$
Because it's well known what kind of curve a hanging cable will describe, and while I don't remember the name right now, I do remember that it's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:27
2
$begingroup$
It's called a catenary.
$endgroup$
– Robert Israel
Aug 21 '18 at 18:29
add a comment |
$begingroup$
It's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:23
$begingroup$
how do you know?
$endgroup$
– combo student
Aug 21 '18 at 18:23
$begingroup$
Because it's well known what kind of curve a hanging cable will describe, and while I don't remember the name right now, I do remember that it's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:27
2
$begingroup$
It's called a catenary.
$endgroup$
– Robert Israel
Aug 21 '18 at 18:29
$begingroup$
It's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:23
$begingroup$
It's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:23
$begingroup$
how do you know?
$endgroup$
– combo student
Aug 21 '18 at 18:23
$begingroup$
how do you know?
$endgroup$
– combo student
Aug 21 '18 at 18:23
$begingroup$
Because it's well known what kind of curve a hanging cable will describe, and while I don't remember the name right now, I do remember that it's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:27
$begingroup$
Because it's well known what kind of curve a hanging cable will describe, and while I don't remember the name right now, I do remember that it's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:27
2
2
$begingroup$
It's called a catenary.
$endgroup$
– Robert Israel
Aug 21 '18 at 18:29
$begingroup$
It's called a catenary.
$endgroup$
– Robert Israel
Aug 21 '18 at 18:29
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
This is a classical problem. The curve is called a catenary, from the Latin word catena, meaning chain. The problem was already circulating around in the days of Galileo. Namely, people asked what shape will a chain take if we let it hang between two fixed points. Hence the name catenary. I read somewhere that Galileo himself thought it must be a parabola, but some other Italian mathematician proved it was not. So if you must make a mistake in a guess, better to make a mistake Galileo made too..
In short, there is no way to circumvent the hyperbolic sine, because it is this function precisely that describes the catenary.
There is a youtube video that claims that the problem you mentioned was given in job-interview for Amazon. IMHO, this is a nice, albeit untrue, story.
answered Aug 21 '18 at 18:32
uniquesolutionuniquesolution
9,3471823
$endgroup$
$begingroup$
It's very hard too just accept the fact that this is not a parabola. I need to find this proof lol
$endgroup$
– combo student
Aug 21 '18 at 18:36
$begingroup$
The proof is in the big cloud up there in the G-heaven. No problem finding it.
$endgroup$
– uniquesolution
Aug 21 '18 at 18:37
$begingroup$
My day is ruined
$endgroup$
– combo student
Aug 21 '18 at 18:42
1
$begingroup$
You didn't get the job at Amazon?
$endgroup$
– uniquesolution
Aug 21 '18 at 18:45
$begingroup$
I couldn't solve this problem so they won't let me do packages for them
$endgroup$
– combo student
Aug 21 '18 at 22:10
add a comment |
$begingroup$
The function that describes a rope affixed at two of it's ends with the only force on it being gravity is called Catenary. On the wikipedia page you'll find all you need to tackle the problem!
answered Aug 21 '18 at 18:29
Davide MorganteDavide Morgante
2,6061726
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
This is a classical problem. The curve is called a catenary, from the Latin word catena, meaning chain. The problem was already circulating around in the days of Galileo. Namely, people asked what shape will a chain take if we let it hang between two fixed points. Hence the name catenary. I read somewhere that Galileo himself thought it must be a parabola, but some other Italian mathematician proved it was not. So if you must make a mistake in a guess, better to make a mistake Galileo made too..
In short, there is no way to circumvent the hyperbolic sine, because it is this function precisely that describes the catenary.
There is a youtube video that claims that the problem you mentioned was given in job-interview for Amazon. IMHO, this is a nice, albeit untrue, story.
answered Aug 21 '18 at 18:32
uniquesolutionuniquesolution
9,3471823
$endgroup$
$begingroup$
It's very hard too just accept the fact that this is not a parabola. I need to find this proof lol
$endgroup$
– combo student
Aug 21 '18 at 18:36
$begingroup$
The proof is in the big cloud up there in the G-heaven. No problem finding it.
$endgroup$
– uniquesolution
Aug 21 '18 at 18:37
$begingroup$
My day is ruined
$endgroup$
– combo student
Aug 21 '18 at 18:42
1
$begingroup$
You didn't get the job at Amazon?
$endgroup$
– uniquesolution
Aug 21 '18 at 18:45
$begingroup$
I couldn't solve this problem so they won't let me do packages for them
$endgroup$
– combo student
Aug 21 '18 at 22:10
add a comment |
$begingroup$
This is a classical problem. The curve is called a catenary, from the Latin word catena, meaning chain. The problem was already circulating around in the days of Galileo. Namely, people asked what shape will a chain take if we let it hang between two fixed points. Hence the name catenary. I read somewhere that Galileo himself thought it must be a parabola, but some other Italian mathematician proved it was not. So if you must make a mistake in a guess, better to make a mistake Galileo made too..
In short, there is no way to circumvent the hyperbolic sine, because it is this function precisely that describes the catenary.
There is a youtube video that claims that the problem you mentioned was given in job-interview for Amazon. IMHO, this is a nice, albeit untrue, story.
answered Aug 21 '18 at 18:32
uniquesolutionuniquesolution
9,3471823
$endgroup$
$begingroup$
It's very hard too just accept the fact that this is not a parabola. I need to find this proof lol
$endgroup$
– combo student
Aug 21 '18 at 18:36
$begingroup$
The proof is in the big cloud up there in the G-heaven. No problem finding it.
$endgroup$
– uniquesolution
Aug 21 '18 at 18:37
$begingroup$
My day is ruined
$endgroup$
– combo student
Aug 21 '18 at 18:42
1
$begingroup$
You didn't get the job at Amazon?
$endgroup$
– uniquesolution
Aug 21 '18 at 18:45
$begingroup$
I couldn't solve this problem so they won't let me do packages for them
$endgroup$
– combo student
Aug 21 '18 at 22:10
add a comment |
$begingroup$
This is a classical problem. The curve is called a catenary, from the Latin word catena, meaning chain. The problem was already circulating around in the days of Galileo. Namely, people asked what shape will a chain take if we let it hang between two fixed points. Hence the name catenary. I read somewhere that Galileo himself thought it must be a parabola, but some other Italian mathematician proved it was not. So if you must make a mistake in a guess, better to make a mistake Galileo made too..
In short, there is no way to circumvent the hyperbolic sine, because it is this function precisely that describes the catenary.
There is a youtube video that claims that the problem you mentioned was given in job-interview for Amazon. IMHO, this is a nice, albeit untrue, story.
answered Aug 21 '18 at 18:32
uniquesolutionuniquesolution
9,3471823
$endgroup$
This is a classical problem. The curve is called a catenary, from the Latin word catena, meaning chain. The problem was already circulating around in the days of Galileo. Namely, people asked what shape will a chain take if we let it hang between two fixed points. Hence the name catenary. I read somewhere that Galileo himself thought it must be a parabola, but some other Italian mathematician proved it was not. So if you must make a mistake in a guess, better to make a mistake Galileo made too..
In short, there is no way to circumvent the hyperbolic sine, because it is this function precisely that describes the catenary.
There is a youtube video that claims that the problem you mentioned was given in job-interview for Amazon. IMHO, this is a nice, albeit untrue, story.
answered Aug 21 '18 at 18:32
uniquesolutionuniquesolution
9,3471823
answered Aug 21 '18 at 18:32
uniquesolutionuniquesolution
9,3471823
answered Aug 21 '18 at 18:32
uniquesolutionuniquesolution
9,3471823
answered Aug 21 '18 at 18:32
uniquesolutionuniquesolution
9,3471823
9,3471823
$begingroup$
It's very hard too just accept the fact that this is not a parabola. I need to find this proof lol
$endgroup$
– combo student
Aug 21 '18 at 18:36
$begingroup$
The proof is in the big cloud up there in the G-heaven. No problem finding it.
$endgroup$
– uniquesolution
Aug 21 '18 at 18:37
$begingroup$
My day is ruined
$endgroup$
– combo student
Aug 21 '18 at 18:42
1
$begingroup$
You didn't get the job at Amazon?
$endgroup$
– uniquesolution
Aug 21 '18 at 18:45
$begingroup$
I couldn't solve this problem so they won't let me do packages for them
$endgroup$
– combo student
Aug 21 '18 at 22:10
add a comment |
$begingroup$
It's very hard too just accept the fact that this is not a parabola. I need to find this proof lol
$endgroup$
– combo student
Aug 21 '18 at 18:36
$begingroup$
The proof is in the big cloud up there in the G-heaven. No problem finding it.
$endgroup$
– uniquesolution
Aug 21 '18 at 18:37
$begingroup$
My day is ruined
$endgroup$
– combo student
Aug 21 '18 at 18:42
1
$begingroup$
You didn't get the job at Amazon?
$endgroup$
– uniquesolution
Aug 21 '18 at 18:45
$begingroup$
I couldn't solve this problem so they won't let me do packages for them
$endgroup$
– combo student
Aug 21 '18 at 22:10
$begingroup$
It's very hard too just accept the fact that this is not a parabola. I need to find this proof lol
$endgroup$
– combo student
Aug 21 '18 at 18:36
$begingroup$
It's very hard too just accept the fact that this is not a parabola. I need to find this proof lol
$endgroup$
– combo student
Aug 21 '18 at 18:36
$begingroup$
The proof is in the big cloud up there in the G-heaven. No problem finding it.
$endgroup$
– uniquesolution
Aug 21 '18 at 18:37
$begingroup$
The proof is in the big cloud up there in the G-heaven. No problem finding it.
$endgroup$
– uniquesolution
Aug 21 '18 at 18:37
$begingroup$
My day is ruined
$endgroup$
– combo student
Aug 21 '18 at 18:42
$begingroup$
My day is ruined
$endgroup$
– combo student
Aug 21 '18 at 18:42
1
1
$begingroup$
You didn't get the job at Amazon?
$endgroup$
– uniquesolution
Aug 21 '18 at 18:45
$begingroup$
You didn't get the job at Amazon?
$endgroup$
– uniquesolution
Aug 21 '18 at 18:45
$begingroup$
I couldn't solve this problem so they won't let me do packages for them
$endgroup$
– combo student
Aug 21 '18 at 22:10
$begingroup$
I couldn't solve this problem so they won't let me do packages for them
$endgroup$
– combo student
Aug 21 '18 at 22:10
add a comment |
$begingroup$
The function that describes a rope affixed at two of it's ends with the only force on it being gravity is called Catenary. On the wikipedia page you'll find all you need to tackle the problem!
answered Aug 21 '18 at 18:29
Davide MorganteDavide Morgante
2,6061726
$endgroup$
add a comment |
$begingroup$
The function that describes a rope affixed at two of it's ends with the only force on it being gravity is called Catenary. On the wikipedia page you'll find all you need to tackle the problem!
answered Aug 21 '18 at 18:29
Davide MorganteDavide Morgante
2,6061726
$endgroup$
add a comment |
$begingroup$
The function that describes a rope affixed at two of it's ends with the only force on it being gravity is called Catenary. On the wikipedia page you'll find all you need to tackle the problem!
answered Aug 21 '18 at 18:29
Davide MorganteDavide Morgante
2,6061726
$endgroup$
The function that describes a rope affixed at two of it's ends with the only force on it being gravity is called Catenary. On the wikipedia page you'll find all you need to tackle the problem!
answered Aug 21 '18 at 18:29
Davide MorganteDavide Morgante
2,6061726
answered Aug 21 '18 at 18:29
Davide MorganteDavide Morgante
2,6061726
answered Aug 21 '18 at 18:29
Davide MorganteDavide Morgante
2,6061726
answered Aug 21 '18 at 18:29
Davide MorganteDavide Morgante
2,6061726
2,6061726
add a comment |
add a comment |
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$begingroup$
It's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:23
$begingroup$
how do you know?
$endgroup$
– combo student
Aug 21 '18 at 18:23
$begingroup$
Because it's well known what kind of curve a hanging cable will describe, and while I don't remember the name right now, I do remember that it's not a parabola.
$endgroup$
– Henrik
Aug 21 '18 at 18:27
2
$begingroup$
It's called a catenary.
$endgroup$
– Robert Israel
Aug 21 '18 at 18:29