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Jogging

Jogging - Physics Forum

Jogging - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.


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  #1  
Old 07-21-2007, 11:03 AM
HVAC
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Default Jogging



One day I decide to go jogging...so at the crack of noon I lace up my
Keds and head out for a jog. I run along a flat road for a while, then
I come to a hill, and run up the hill. Once at the top, I immediately
realize the folly of my efforts, and immediately head back down the
hill, following the exact same path back to my house where I realize I
have been gone exactly 2 hours.

Now, here's the question. Running on flat ground I can make
8mph...going uphill I am traveling at 6mph, and going downhill I am
covering 12mph.

The question is...How far have I jogged in those 2 hours?

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  #2  
Old 07-21-2007, 01:23 PM
Lord Turkey Cough
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"HVAC" <[Only registered users see links. ]> wrote in message
news:1185015826.166092.188800@n60g2000hse.googlegr oups.com...

You have not jogged anywhere, as you are at the centre of the universe,
as I proved earlier.




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  #3  
Old 07-21-2007, 01:23 PM
Lord Turkey Cough
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"HVAC" <[Only registered users see links. ]> wrote in message
news:1185015826.166092.188800@n60g2000hse.googlegr oups.com...

You have not jogged anywhere, as you are at the centre of the universe,
as I proved earlier.




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  #4  
Old 07-21-2007, 03:36 PM
Aaron
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Default Jogging


"HVAC" <MR.HVAC@gmail.com> wrote in message
news:1185015826.166092.188800@n60g2000hse.googlegr oups.com...

This is the classic Physics 1/A trick question when they teaching you the
concept of vector units.

In two hours you went nowhere. Zero.

In practice, since for the intents that it is applied, basic physics applies
to a world with 3 dimensions of freedom for movement.

So at any "instant" the speed the first derivative of a function which maps
time elapsed since you started to displacment from where you started. You
could represent this by the length of a straight line or the sum three
vectors, one for each dimension, right?

If you want to know the length of the imaginary lines on the ground you
made, then you need to integrate that entire function, which you are going
to need GPS for. Or if you use the values in the question I'd guess it was
more of an algebra problem, and I don't even like to think about algebra I
use mathematica

I think the answer you are looking for is the fact that average velocity is
the displacement from origin divided by the time of the "jog". Since at the
end you were back where you started, you are dividing the time, which no
matter how long, into zero displacement and everybody knows that zero
divided by anything is still zero - actually it's not a mathematical truth,
it's just a concept to keep math people from going insane. Zero is a
concept, not a quantity.




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  #5  
Old 07-21-2007, 03:36 PM
Aaron
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Default Jogging


"HVAC" <MR.HVAC@gmail.com> wrote in message
news:1185015826.166092.188800@n60g2000hse.googlegr oups.com...

This is the classic Physics 1/A trick question when they teaching you the
concept of vector units.

In two hours you went nowhere. Zero.

In practice, since for the intents that it is applied, basic physics applies
to a world with 3 dimensions of freedom for movement.

So at any "instant" the speed the first derivative of a function which maps
time elapsed since you started to displacment from where you started. You
could represent this by the length of a straight line or the sum three
vectors, one for each dimension, right?

If you want to know the length of the imaginary lines on the ground you
made, then you need to integrate that entire function, which you are going
to need GPS for. Or if you use the values in the question I'd guess it was
more of an algebra problem, and I don't even like to think about algebra I
use mathematica

I think the answer you are looking for is the fact that average velocity is
the displacement from origin divided by the time of the "jog". Since at the
end you were back where you started, you are dividing the time, which no
matter how long, into zero displacement and everybody knows that zero
divided by anything is still zero - actually it's not a mathematical truth,
it's just a concept to keep math people from going insane. Zero is a
concept, not a quantity.




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  #6  
Old 07-21-2007, 05:25 PM
OG
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Default Jogging


"HVAC" <[Only registered users see links. ]> wrote in message
news:1185015826.166092.188800@n60g2000hse.googlegr oups.com...


A velocity - time graph is a very useful tool here, there are 4 rectangles
for the 4 phases of the jog, and knowing that the area under the graph gives
the distance travelled gives the solution.

On the other hand, I got within an ace of proving to myself that you can't
actually tell because the distance depends on how much time you spend on the
flat, but fortunately I checked my 'upper and lower limits' and found that
all variants give the same result.

Sadly, only 6.5 / 10 for me then.




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  #7  
Old 07-21-2007, 05:25 PM
OG
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Default Jogging


"HVAC" <[Only registered users see links. ]> wrote in message
news:1185015826.166092.188800@n60g2000hse.googlegr oups.com...


A velocity - time graph is a very useful tool here, there are 4 rectangles
for the 4 phases of the jog, and knowing that the area under the graph gives
the distance travelled gives the solution.

On the other hand, I got within an ace of proving to myself that you can't
actually tell because the distance depends on how much time you spend on the
flat, but fortunately I checked my 'upper and lower limits' and found that
all variants give the same result.

Sadly, only 6.5 / 10 for me then.




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  #8  
Old 07-21-2007, 05:26 PM
OG
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Default Jogging


"HVAC" <[Only registered users see links. ]> wrote in message
news:1185015826.166092.188800@n60g2000hse.googlegr oups.com...

and we all end up cross posting to a bunch of cranks on other newsgroups.


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  #9  
Old 07-21-2007, 05:26 PM
OG
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Default Jogging


"HVAC" <[Only registered users see links. ]> wrote in message
news:1185015826.166092.188800@n60g2000hse.googlegr oups.com...

and we all end up cross posting to a bunch of cranks on other newsgroups.


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  #10  
Old 07-22-2007, 12:53 AM
OG
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Default Jogging


"Rich Corinthian Leather" <[Only registered users see links. ]> wrote in message
news:Cuxoi.3447$[Only registered users see links. ].prodigy.ne t...

And apart from being a comprehensive answer the only problem is that it's
wrong.

You know from the text that he ran the same DISTANCE uphill as downhill, but
your calculation implies that he spent the same TIME doing both. Your
calculation implies that the hill was twice as long going down as going up.

My guess is that you're either a
alien research kinda guy
or a paranormal kinda guy
or a crop-circle kinda guy

I'll be happy to continue discussions with atheists and alt.physicists


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