A Time puzzle to solve...

[419]

No. Because I couldn't be fagged.

Fair enough.

I'm sure you must be exhausted after this sort of precision answering your own general question about the position of the hands on an unspecified analog clock with an unspecified movement and commenting on the accuracy, deficiencies or otherwise of those who answered your problem.

Every second the M hand moves 0.1°, and the H hand moves 1/12 of that, or 0.083333 repeater°
So if H starts at 30° and s is the seconds until M = H then
30 + 0.083333 * s = 0 + s * 0.1
Multiply both by 10 ► s = 300 + s*0.83333

or ► s = 300 + s/12
Multiply both by 12 ► 12s = 300*12 + s
so ► 11s = 3600
so ► s = 3600/11
= 327.73 seconds later
or 1:00 plus 327.73 seconds which is 1:05 and 27.73 seconds.

Or could it be that it is impossible to identify the position of the hands on a non-quartz movement analog clock except by observation of a given clock because the machining and tensions and inter-operation of the various parts introduces unknown and incalculable variables which were not contemplated by the problem and formulas you posed?

No need to respond if you actually don't think you care or couldn't be fagged.

Just a bit of fun.

[mic-d]

Thank you FF for posting these maths related quizzes and taking the time to provide answers. It's got the grey matter working on logic and recall of high school maths which I'm grateful for. I hope you keep posting them when you have time.

And no need to begin with a long preamble about how this is an idealised situation and provide 25 caveats, it's implicit that it's the ideal case. Could you imagine an exam question written like that! Or how Einstein would have got around to explaining his theories of relativity if people piped up with 'wait, but is the train steam, electric or diesel, or my god, is it diesel-electric, and is there a nice restaurant car on it that serves a good BLT sandwich?' or 'is the rocket ship solid or liquid fuelled, does it have Netflix to make the time go faster?'

I see cheekiness in this post (the quartz clock) but also nastiness in the form of a Straw Man argument (the mechanics of a clock) designed to impugn the strength of your question, it's a compensation mechanism by those who couldn't or wouldn't solve it, much in the way a flash sports car is compensation for ED.

[yvan]

All I can say is none of the answers are right so far. The time will obviously have to be between 1:05 and 1:10 though.

And it's not a Mondial clock, because that would take the fun out out of it.

All I can say is Thank God for digital timepieces !!!
I haven't got the time to figure out at what precise time one hand is over the over, at whatever hour...
As the piece's movement is continuous, I can only estimate that yours is a trick question!
For a milli-second there I thought I had the answer but the bloody thing moved again....

All I can say is we'll get to Xmas on the 25th.

Merry Christmas
Yvan

[Boringgeoff]

Reminds me of the time a policeman pulled me up and accused me of failing to stop at a stop sign. I explained to him the physics of an insect hitting your windscreen head on, in the split second between when the insect is flying forwards until it starts going backwards there is a moment when it is stationary, at this precise moment the vehicle is also stationary. Needless to say, the policeman was not impressed by my brilliant scientific knowledge and the ticket was duly written.

Cheers,
Geoff.

[ian]

The original question doesn't limit the type of analog clock to a quartz movement, unless one interprets 'regular' in the question to mean as regular as a quartz movement as distinct from a 'regular' 12 number clock face.

If the latter, then it includes clocks with mechanical movements, the accuracy of which depend upon the quality of manufacture of the gears and springs etc.

"regular" in horological terms refers to the escapement mechanism invented by John Harrison around 300 years ago. The escapement mechanism allowed the spring spring tension to be released in a controlled manner so that the hands on a regulated clock always move at a constant speed regardless of the spring tension.


Horology is the study and measurement of time and the art of making of clocks and watches.

[FenceFurniture]

Yes, I guess that makes John Harrison the father of "proper" navigation. You'd think they'd have the decency to call at Harrology wouldn't you?

[ian]

Yes, I guess that makes John Harrison the father of "proper" navigation. You'd think they'd have the decency to call at Harrology wouldn't you?

Horology has been the term used for the study of time and clocks for a very very long time.

The book Longitude by Dava Sobel tells the story of how Harrison solved "the greatest scientific problem of Harrison's time"
I highly recommend the book.

[FenceFurniture]

I am not going to consider:

• the time it takes M to accelerate and decelerate in its 6° travel in 1/16 second – it's unknown anyway
• anything to do with quartz
• wear and tear, age, quality, country of manufacture, the weight of any dust on the hands, wind direction, gravitational pull, La Niña effect or any other such ridiculous, pedantic notion to satisfy the 81st Prime Number

Assumptions:

1. M starts moving at the very end of each 60 second period, rather than at 59 and 15/16 seconds (i.e. a 1/16 sec before the minute has finished).
2. M and H are both symmetrical in their width shape, and are straight

Givens:

1. We know that at 1:05 plus 1/16 seconds, M is at the 30° position, and that it only moves every 60 seconds.
2. We know that at 1:06, M is still at the 30° position, but 1/16 second later it is at 36°.
3. We know that at 1:05, H is at the 32.5° position, and that it advances at a rate of 0.5° per minute or 1/120° per second.

Thus, at 1:06:00, H has moved to 33.0°, and 1/16 seconds later it has moved 1/120/16° or 0.00052° (rounded) and will be at 33.00052°

So when will M be at 33.00052°?
A 1/16 second is 0.0625 seconds so it has to be a little over half of that time to move a little over half the distance (3.00052° of 6° travel)
So 3.00052 / 6 * 0.0625 = 0.03125542534 seconds
At 1:06 plus 0.03126 seconds to the nearest 1/10,000 sec is when the centre of M passes across the centre of H, or more realistically phrased as 1:06 plus 1/32 seconds (in other words plus half the 1/16 second it takes to click forward).

[ian]

I am not going to consider:

• the time it takes M to accelerate and decelerate in its 6° travel in 1/16 second – it's unknown anyway
• anything to do with quartz
• wear and tear, age, quality, country of manufacture, the weight of any dust on the hands, wind direction, gravitational pull, La Niña effect or any other such ridiculous, pedantic notion to satisfy the 81st Prime Number

Doses that mean that you will allow the coriolis force to apply ??





more [possibly] when I have the time

[FenceFurniture]

I see cheekiness in this post (the quartz clock)

Agreed.

but also nastiness in the form of a Straw Man argument (the mechanics of a clock) designed to impugn the strength of your question, it's a compensation mechanism by those who couldn't or wouldn't solve it, much in the way a flash sports car is compensation for ED.

Also agreed. Real fun stuff, and completely uncalled for.


For clarity (definitions from internet search):
accurate adjective (especially of information, measurements, or predictions) correct in all details, exact

So giving rise to "as accurate as possible" if it can't be exact or precise, and not to be confused with

pedantic adjective excessively concerned with minor details or rules; over-scrupulous. Pointing out minor errors, correcting people who make small mistakes, and bragging about their own knowledge and expertise

[FenceFurniture]

Doses that mean that you will allow the coriolis force to apply ??





more [possibly] when I have the time

[GraemeCook]

... The book Longitude by Dava Sobel tells the story of how Harrison solved "the greatest scientific problem of Harrison's time"
I highly recommend the book.

I totally endorse Ian's recommendation. It was a major research project. Before that, coasts were discovered by running into them ... literally.

A major part of Cook's Endeavour voyage was trialling a chronometer. Did it work in practice as well as in theory? It did.

The French were also equally involved in similar research. On d'Entrecasteaux's voyages some 20 years later he carried 14 chronometers (# from memory). The Brits wanted to know if chronometers actually worked, the French wanted to know which was best! Science was advancing rapidly.

[rwbuild]

.....at the third stroke the time will be..ah bugger.....at the fourth stroke the time will be..ah bugger.....at the fifth.... bugger it, lets have a beer instead

[FenceFurniture]

.....at the third stroke the time will be..ah bugger.....at the fourth stroke the time will be..ah bugger.....at the fifth.... bugger it, lets have a beer instead

That guy, with his BBC accent, is long gone! So is the service.

[yvan]

.....at the third stroke the time will be..ah bugger.....at the fourth stroke the time will be..ah bugger.....at the fifth.... bugger it, lets have a beer instead

Quite right! A few sherberts later and time doesn't matter any more!
I'll have to ask FF is this qualifies as an answer to his original trick question