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Of dogs and men


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19 replies to this topic

#11 TimeSpaceLightForce

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Posted 18 April 2013 - 01:47 PM

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#12 bonanova

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Posted 19 April 2013 - 08:18 AM

k-man and TSLF agree on an answer that differs slightly from mine.
So as it stands I am outvoted.
 
But I invite a critique of my solution.
 

Spoiler for Here it is


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#13 bushindo

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Posted 23 April 2013 - 03:34 PM

k-man and TSLF agree on an answer that differs slightly from mine.
So as it stands I am outvoted.
 
But I invite a critique of my solution.
 

Spoiler for Here it is

 

bonanova's work checks out to me. I used k-man and TSLF's answers and worked backward to get a distance of about 50.4 feet moved, so I'm casting a vote for bonanova.


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#14 bushindo

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Posted 23 April 2013 - 06:25 PM

Spoiler for estimate at a first glance

 

I think there's an error here (see part highlighted in red above)

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#15 k-man

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Posted 23 April 2013 - 06:45 PM

 



Spoiler for estimate at a first glance

 

I think there's an error here (see part highlighted in red above)

Spoiler for

 

 

You're right. I made a wrong assumption here and that's what amounts to the difference in the answers. I'm convinced that Bonanova's solution is correct.


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#16 TimeSpaceLightForce

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Posted 23 April 2013 - 09:04 PM

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#17 bonanova

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Posted 24 April 2013 - 11:41 AM

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Was that the assumption you made in your graphical solution?


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#18 TimeSpaceLightForce

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Posted 24 April 2013 - 04:57 PM

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#19 bonanova

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Posted 25 April 2013 - 03:19 AM

OK I see what you did.

 

It seems more natural to assume the same thing for the dog that one assumes for the men.

The men march at a constant speed; the dog trots at a constant speed.

The men's feet are in contact with the ground; the dog's feet are in contact with the ground.

 

If we were talking about an airplane, then both airspeed and ground speed are of importance.

If we were talking about a boat, then both water speed and "geographical" speed are of importance.

 

If the dog's feet were somehow in contact with the men, a "soldier speed" would have import.

 

That might happen as follows:

Imagine the soldiers are carrying a 100' x 100' platform on their shoulders.

A dog runs at constant speed around the perimeter of the platform.

Now constant speed would mean with respect to the soldiers.

What is the distance traveled by the dog?

 

With respect to the platform, exactly 400'

With respect to the ground, something like your answer.


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- Bertrand Russell

#20 TimeSpaceLightForce

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Posted 25 April 2013 - 08:20 AM

There are no absolute speeds only relative..In this case , there were 3 inertial frames involved: the ground , the phalanx and the dog.

they are all have a change in distance per time and whether they touches or not it does not matter..the dog in the platform will find it

easier to run around the outside of the square but still relative to the observer on the ground the elevated dog has 3 variable speeds

according to his own reference frame. Even if he is on a steady hot air balloon 1 m above the ground. Thus,any constant speed should

be referenced..

 

I see that you computed it correctly .. using the constant speed relative to the ground and now its clear why K-man and my graph data differs.

 

another good puzzle!


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