TIME!!
Hi everyone !
Well now that pre-boards are over hopefully there will be more of problem solving on this blog.
Here's an interesting question: Short and simple.
How many times are the hands of a clock at right angles in a day ?
(P.S. It is definitely more than 2 times)
Well now that pre-boards are over hopefully there will be more of problem solving on this blog.
Here's an interesting question: Short and simple.
How many times are the hands of a clock at right angles in a day ?
(P.S. It is definitely more than 2 times)
posted by AJ at 6:12 PM
5 Comments:
A Tough one there , still thinking
I think i've got it ...but am not sure of the answer...
The velocity of hour hand is 2pi/12*60*60 rad/sec..
and the velocity of minute hand is 2pi/60*60...
their relative velocity is 22pi/12*60*60 rad/sec...
Angle covered in t time is (2n+1)pi/2...
Equate to get different times....
Answers are 3/11 hrs, 9/11 hrs, 1 (4/11) hrs,...and so on.. (3n/11 where n is an odd integer..)
Here we are talking of only hour and the minute hand.
i know the answer -its 44. That should help you out...keep thinking..I got it a week after i saw this problem..and the answer's confirmed.I'll post the solution in few days till then lets see if someone else comes with an explanation.
here i am assuming that you are obviously referring to the hour and minute hand of the clock. had you also taken the seconds hand into account this would have become really complicated. anyway here it is.
the answer is 44
in order to give the solution i am devising a computer program. it'll be ready shortly and i'll post the link here. what it'll do is that it'll prove that in one hour an angle of 90 is made exactly twice, so there are 24 hours which gives 48 such instances but we will not take into account the 4 times 90 is made at 3 and 9 o clock obviously.
You are right but who are you??
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