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#1 2012-12-31 00:28:57

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
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Clock Problem

Question 1: How to find the angle between the two hands of the clock at a given time?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#2 2012-12-31 00:45:48

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
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Re: Clock Problem

Hi Agnishom

The angle is |h*30°-(m/2)*11°-(s/120)*11°|


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
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#3 2012-12-31 01:51:45

Agnishom
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Re: Clock Problem

Sorry, it had been too stupid question

A clock is set right at 7 am. The clock gains 10 minutes in 24 hrs. What will the approximate time when the clock indicates 1 pm on the following day?

Is it 12:47:30 pm?

Last edited by Agnishom (2012-12-31 01:53:18)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#4 2012-12-31 02:03:09

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,922

Re: Clock Problem

That is correct.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#5 2012-12-31 02:13:54

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,572
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Re: Clock Problem

Now, how do I show that the hands of the clock come in right angles 22 times?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#6 2012-12-31 02:17:33

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,922

Re: Clock Problem

They do not. They are at right angles much more times. 46 times, I would say...


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#7 2012-12-31 02:26:57

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,572
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Re: Clock Problem

Then 22 is the number of what?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#8 2012-12-31 02:31:52

bob bundy
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Registered: 2010-06-20
Posts: 7,020

Re: Clock Problem

Maybe that is for 90 measured clockwise (the rest 270)  ?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2012-12-31 02:36:38

bob bundy
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Registered: 2010-06-20
Posts: 7,020

Re: Clock Problem

Changed my mind.  I think it is 22.

00.15 
0045
01.15 and a bit
01.45 and a bit
.......

2 per hour

but as the hour hand advances you loose the last hour

so 11 hours at 2 per hour.

Stefy:  Is your clock a 24 hour one?  ie 23 x 2 = 46

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2012-12-31 04:13:53

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,922

Re: Clock Problem

Actually, it is neither. We need to be given a time period on which we count the right angles...


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#11 2012-12-31 05:32:36

scientia
Member
Registered: 2009-11-13
Posts: 224

Re: Clock Problem

I think the problem is for a 12-hour period. The simplest way is to count how many times the hands are at right angles in every hourly.

00:00 to 01:00 – 2
01:00 to 02:00 – 2
02:00 to 03:00 – 2 (including 3 o'clock)
03:00 to 04:00 – 1
04:00 to 05:00 – 2
05:00 to 06:00 – 2
06:00 to 07:00 – 2
07:00 to 08:00 – 2
08:00 to 09:00 – 2 (including 9 o'clock)
09:00 to 10:00 – 1
10:00 to 11:00 – 2
11:00 to 12:00 – 2

The hands are at right angles twice every hourly except for the hours 03:00–04:00 and 09:00–10:00. So it's 22 times every twelve hours.

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#12 2012-12-31 06:34:26

scientia
Member
Registered: 2009-11-13
Posts: 224

Re: Clock Problem

Oh, here's the math.


The angular velocity of the minute hand is 6° per minute and that of the hour hand 0.5° per minute. The difference in their angular velocities is therefore 5.5° per minute. Starting at twelve o'clock, the time taken for the hands to be first at right angles with each other is 90/5.5 minutes. Thereafter the minute hand has to turn through 180° to be next at right angles with the hour hand; the time taken for this is 180/5.5 minutes. If
is the time in minutes at which the hands are perpendicular for the
th time after twelve o'clock, we have the formula:

There are 720 minutes in half a day. The largest integer

for which
is
.

Happy New Year! smile

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#13 2012-12-31 06:53:27

scientia
Member
Registered: 2009-11-13
Posts: 224

Re: Clock Problem

And these are the times at which the hands are perpendicular (using 12-hour notation):






















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#14 2012-12-31 17:36:47

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,572
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Re: Clock Problem

Got it! Happy New Year!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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