Bouncing a question of the resident DU experts

[SinkingInTheRain]

If a stopped clock is right twice a day then what is the duration of the stopped clock being right?

For extra credit; How much time does an arrow shot into the sky spend between going up and coming down at the apogee.

[SOteric]

1. Foremost in compiling my calculation is the burning question

'Why do we need to know?'

[SinkingInTheRain]

3. Time travel

Answer the question and you're there.

[Birthmark]

2. 1,438 minutes

And if memory serves, 86,398 seconds.

[SinkingInTheRain]

4. Wrong

86,398 - 86,398 would be closer to the answer than anyone has come.

[TreasonousBastard]

5. The stopped clock...

is accurate twice a day at a point. A point, by definition, is immeasurable, whether in time or space. In practical terms, it's accurate to the degree of measurement desired-- a second, a millisecond... whatever.

I haven't the foggiest idea how to calcualte the other one. I am not going to dig out old texts to remind myself how to calculate the deceleration going up and the acceleration coming back down, although I seem to remember it's not that difficult.

[SinkingInTheRain]

6. It's beyond difficult

It's unsolved. The time granularity is infinite and can't be measured unless you can stop or reverse time. It is a problem that is being worked on as we speak...

[dweller]

7. Politics ain't Poetry, but i'll try

The Calculation
A man six feet tall stands on a curb, facing a light suspended fifteen feet above the middle of a street thirty feet wide. He begins to walk along the curb at five m.p.h. After he has been walking for ten seconds, at what rate is the length of his shadow increasing?
A problem posed by my calculus instructor, Penn State, 1946

Facing a streetlight under batty moths
And June bugs ratcheting like broken clock springs,
I stand, for the sake of a problem, on the curb--
Neither in grass nor gutter--while those wings
Switch down the light and patch my undershirt.

I turn half right. My shadow cuts a hedge,
Climbs through the rhododendrom to a porch,
And nods on a window sill. How far it goes
I leave to burglars and Pythagoras.
Into the slanting glare i slant my watch,

Then walk five miles per hour, my shoes on edge
In a practiced shuffle past the sewer grid,
over the gold no-parking-or-pausing zones,
And into the clear--five seconds--into dirt,
Then over a sawhorse studded with lanterns,

And, at the tenth, i stiffen like a stump
Whose lopped head ripples with concentric figures,
Note the location of my other head
In a garden, but keep trundling forward,
Ignoring Doppelgangers from moon and lawn-lamp,

My eyes alert now, levelling my feet,
Seeing my shadow sweeping like a scythe
Across the stalks of daisies, barking trees
And scraping up the blistered weatherboard
To the eaves of houses, scaling the rough shingles.

At fifteen seconds, in a vacant lot,
My head lies on a board. I count it off.
I think back to the garden, and I guess,
Instructor, after fifteen years of sweat,
It was increasing five feet plus per second.

At the start, I could have fallen, turned around
Or crossed to the very center of confusion,
My shadow like a manhole, no one's length,
Or the bulb itself been broken with a shot,
And all my reckoning have gone unreckoned.

But I was late because my shadow was
Pointing toward nothing like the cess of light,
Sir, and bearing your cold hypotenuse--
That cutter of corners, jaywalker of angles--
On top of my head, I walked the rest of the night.

David Wagoner


2 seconds, infinitely.
dp

[SinkingInTheRain]

8. Speaking of Time...

Ticking away the moments that make up a dull day
You fritter and waste the hours in an offhand way.
Kicking around on a piece of ground in your home town
Waiting for someone or something to show you the way.

Tired of lying in the sunshine staying home to watch the rain.
You are young and life is long and there is time to kill today.
And then one day you find ten years have got behind you.
No one told you when to run, you missed the starting gun.

So you run and you run to catch up with the sun but it's sinking
Racing around to come up behind you again.
The sun is the same in a relative way but you're older,
Shorter of breath and one day closer to death.

Every year is getting shorter never seem to find the time.
Plans that either come to naught or half a page of scribbled lines
Hanging on in quiet desperation is the English way
The time is gone, the song is over,
Thought I'd something more to say.

[Rabrrrrrr]

9. It is correct for dt amount of time

that is, delta t, the differential amount, the smallest amount possible, which I can't explain any better, but if you studied calculus, you'll know what it means.

And at the apogee, an arrow spends zero amount of time.

[Donkeyboy75]

10. It depends on the way one measures time.

Time is a relative thing. If you are using a clock with gears to measure time, then it is the amount of time that the gear which controls the second hand of the clock you are measuring with spends in any one groove of said gear.

If you are somehow using molecular bond vibrations to keep time...about one femtosecond (or .000000000000001 second). It hasn't yet been proven that there is a unit of time that cannot be divided into smaller units of time.

[AZCat]

11. In posting these questions, you are falling into a common trap

Most people assume that time is linear- but as SOs the world over have discovered, "Just 5 minutes" is really about half an hour.

So while the 'technically correct' answers have been posted above, I question the logic that has led to these conclusions.

Y'see, I happen to have TWO stopped clocks in my apartment (yes, I am a bachelor). Therefore, my stopped clocks are right ALL THE TIME since I can confirm the correctness of their reading by examining the other clock. But since I have yet to determine exactly how long my day is, I cannot give you a numerical answer.

As to your arrow question, 'up' and 'down' are relative, and I refer you to speeches of any of the outspoken members of the Bush Administration for a lesson in this. It is important to determine whether or not the arrow has WMD, because this will tell if it is being truthful about how much time it spends going 'up' or 'down'. There are those who will claim that 'up' and 'down' are really the same direction and that the time in the middle has been shipped over the border into Syria. I will leave you to your own conclusions.

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