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Santa Claus's speed


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19 replies to this topic

#11 TimeSpaceLightForce

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Posted 25 March 2014 - 05:11 PM

 

Spoiler for

True but this task is about moving as slow as possible.  Though he can travel that fast, which is how he is able to deliver all those christmas gifts, we want to know what is the slowest he could go.

 

Well i don't know.. i  read about  the twin brothers where one travel at relativistic speed.. and when he returned the brother that stayed got much older.. What i do not get or missing is "why are we assuming he can travel faster than light?"


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#12 BMAD

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Posted 25 March 2014 - 05:51 PM

 

 

Spoiler for

True but this task is about moving as slow as possible.  Though he can travel that fast, which is how he is able to deliver all those christmas gifts, we want to know what is the slowest he could go.

 

Well i don't know.. i  read about  the twin brothers where one travel at relativistic speed.. and when he returned the brother that stayed got much older.. What i do not get or missing is "why are we assuming he can travel faster than light?"

 

 

I believe the American term is that it is a Red Herring.  Just because my car can travel 90mph doesn't mean that I will or should.  So just because Santa Clause could travel faster than the speed of light doesn't mean he will or should.  He may need to on December 25th in order to deliver the presents but otherwise he would probably prefer a leisurely trip as he goes south for his vacation.


Edited by BMAD, 25 March 2014 - 05:52 PM.

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#13 TimeSpaceLightForce

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Posted 28 March 2014 - 03:38 PM

Spoiler for

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#14 BMAD

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Posted 28 March 2014 - 05:40 PM

 

Spoiler for

 

Can he go slower?


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#15 bonanova

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Posted 28 March 2014 - 06:42 PM

Define "going slower." What does it mean?

  1. Longer elapsed time before reaching South Pole
    We could find an arbitrarily long path and define speed = (distance between poles)/(elapsed time.)
    This definition gives one value of speed for the entire trip and does not depend on the layout of the path.
    We could go slower under this definition by flying endlessly at night at a constant latitude.

     
  2. Lower path speed.
    This means speed = ds/dt where s is path length.
    Here speed is an instantaneous value.
    With this definition we could go slower just by stopping to rest for a while.
    That is, we could make our (instantaneous) speed zero. That is very slow.

Also define "best path."

 

I think of best path as most efficient - shortest path or earliest arrival.

Going slower seems to ask for the path that will tire him the least.

 

So, instantaneous speed, average speed, longest transit time, shortest path, rest stops for the reindeer to regain strength, least time between houses so children don't have to wait for their toys, lowest to the ground so everyone can hear HO HO HO clearly ... there are a lot of things that might make a path "best."


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#16 BMAD

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Posted 28 March 2014 - 06:52 PM

Assuming that Santa must always get progressively closer to the south pole.  What is the slowest (longest duration of travel) he can travel and remain forever at night?  So far both you (bonanova and TSLF) claim it is 1 year.  I am asking if this is correct.


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#17 harey

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Posted 28 March 2014 - 10:14 PM

Spoiler for @plasmid

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#18 harey

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Posted 28 March 2014 - 10:31 PM

Assuming that Santa must always get progressively closer to the south pole.  What is the slowest (longest duration of travel) he can travel and remain forever at night?  So far both you (bonanova and TSLF) claim it is 1 year.  I am asking if this is correct.

 

I am assuming we are looking for the smallest CONSTANT speed.

 

If we want to maximize the travel time (at varying speed), he can travel almost forever: he follows the shadow line moving imperceptibly to the south.


Edited by harey, 28 March 2014 - 10:34 PM.

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#19 BMAD

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Posted 28 March 2014 - 10:46 PM

Define "going slower." What does it mean?

  • Longer elapsed time before reaching South Pole
    We could find an arbitrarily long path and define speed = (distance between poles)/(elapsed time.)
    This definition gives one value of speed for the entire trip and does not depend on the layout of the path.
    We could go slower under this definition by flying endlessly at night at a constant latitude.

     
  • Lower path speed.
    This means speed = ds/dt where s is path length.
    Here speed is an instantaneous value.
    With this definition we could go slower just by stopping to rest for a while.
    That is, we could make our (instantaneous) speed zero. That is very slow.
Also define "best path."
 
I think of best path as most efficient - shortest path or earliest arrival.
Going slower seems to ask for the path that will tire him the least.
 
So, instantaneous speed, average speed, longest transit time, shortest path, rest stops for the reindeer to regain strength, least time between houses so children don't have to wait for their toys, lowest to the ground so everyone can hear HO HO HO clearly ... there are a lot of things that might make a path "best."

I do not know if you recognize it but this is a variation of one of your puzzles (I believe a year old now?). You asked us to try and solve a travel salesman problem that maximized travel as one moved progressively closer to their target. Mine is similar to yours except yours was movement on a grid.
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#20 plasmid

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Posted 29 March 2014 - 05:11 AM

I chose to define "best path" as the path which gets Santa from the North pole to the South pole with the lowest possible top speed at any point in the path, neglecting the tilt of the Earth (and hence possibility of one pole being in constant daylight). This seemed to be the definition that makes the problem non-trivial.

If you consider the way it's phrased in post #16, asking what the longest duration of travel Santa could make while staying in darkness, then I agree with harey's answer, but I suspect that BMAD meant something else.
 

Spoiler for @plasmid

Comments are within the spoiler, although I somehow get the feeling that maybe you were trying to make a point that I'm not picking up on?

Edited by plasmid, 29 March 2014 - 05:18 AM.

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