Clock Work
posted by Rajesh Lal at
1:11 AM
Tuesday, October 28, 2008
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22 Comments:
7:05:16
5 mins and 16 seconds past 7
i think.............
6pm...some might think 12:30pm, but the little hand would be halway between the 12 and 1 thereby not making a 180 degree angle.
12:32.32
32 mins and 32 seconds to 12
It is 12:32:43
27 mins and 17 seconds to 1
32 mins and 43 seconds past 12
Each 1 hour, 5 minutes and 27.27 seconds after 6 o'clock, the angle between the minute and hour hand of a clock is 180 degrees
ehh... 7:05 pm i guess o.o
I'm gonna go with 7:05:27 a.m.
Drake
7:05:28
hjg
it would be 6:00am and 1 second
The path of the clock hand is periodic, meaning it repeats itself after a certain amount of time; therefore it can be represented as a sinusoidal function.
Let y=cos(2pi*t) be the minute hand
Let y=cos(pi/6*t) be the hour hand
where t is the time in hours
When the hands are 180 degrees (pi radians) apart, one hand ill be positive and the other hand will be negative meaning their sum is 0. So the function is 0=cos(2pi*t)+cos(pi/6*t).
The solution is t=(12n+6)/11 where n is the set of integers.
So when t=6, n=5; so the next value for n is 6. When n=6, t=7.090909 hours or rather 7:05AM and 27 seconds. (to be more precise, 7 hours 5 minutes and 27.27 seconds)
There is an ambiguous solution when t=(12n+6)/13. This occurs when the hands of the clock are on the same side and the sum of their angles is 0.
you can also look at the clock widget in vista and see when the hands are 180 degrees apart
this 180 degrees apart phenomenon happens exactly 11 times for each 12 hours: from 6am to 6pm, it'll occur at 7+,8+,9+,10+,11+,12+,1+,2+,3+,4+, then 6pm.
so the period is 12/11 hours or 1hr 5min 27sec.
Clock Work
At precisely 6:00 AM the angle between the minute
and hour hand of a clock is 180 degrees. To the
nearest second, what time will it be when the
angle between the two hands is again 180 degrees?
LHrate=360/60 ;long hand moves at 1 revolution
or 360 degrees per 60 minutes
SHrate=360/12/60 ;short hand moves 1/12th of a
revolution per 60 minutes
;After x minutes the long hand will have moved
x*LHrate, the shorthand will
have moved x*SHrate
;Beginning with the Long hand at 0 degrees and
the short hand at 180 degrees; how long will it be
;before there's 180 degrees seperation again?
Equations
LH=x*LHrate
SH=180+x*SHrate
LH-SH=180
;then LH = 392.727272727 and SH = 212.7272727272
;answer x = 65.454555 minutes
Seconds=(x-int(x))*60 ; Seconds = 27.272727...
; time will be 7:05:27 to the nearest second
hjg
Also, at precisely 9:15 AM/PM, or 3:45AM/PM. :)
xoxo
bre
6:00 PM ???
6:01? :S
7:05:05
5 Minutes and 5 seconds past 7. The second hand gradually moves the minute hand, as it moves the hour hand. (At half past 8 the hour hand is in between the 8 and 9, as is the minute hand at 30 seconds past any minute). Ergo, at 7:05:05, the hour hand would have moved the same amount past the 7 as the minute hand has moved past the 1(indicating 5 past).
6:00 PM
I don't have any idea what Sam is talking about but he sounds really smart.
this thing happens whan a simple question is given to complex minds!
right sam?!
nice one!!
It is between 10 o'clock and 11 o'clock, and the hands of a clock are 180 degrees appart. What time is it? Please I'm desperate for help, this is my HOMEWORK! x
my homework says:
at 20 minutes to 2 the clock hands are almost but not quite pointing at exactly opposite directions. at what time, closest to 20 to 2 are the hands in exactly the opposite direction?
i found out its around 1:38 and some seconds but i need to show working out and i dont have anthing to write for that...
HELP PLZ!!!!
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