this one is so good (and not solved) I pulled it foreward in time
Posted by quizzical on Thursday, November 16, 2006 at 6:24am.
This is just a question that has stumped me for some time:
We have a normal watch.
The big hand is 4cm long and the little hand is 3cm long.
What's the distance between the tips of the hands at the moment they are moving the fastest towards each other.
For Further Reading
* math Puzzler.. - bobpursley, Thursday, November 16, 2006 at 9:24am
5 cm. Think out why.
o math Puzzler.. - Lance, Thursday, November 16, 2006 at 11:53am
Facinating question. I don't get it? Say the clock was 20 feet in diameter. Please enlighten me.
* math Puzzler.. - Ken, Thursday, November 16, 2006 at 12:02pm
is that the moment of change between obtuse and acute exchange between the angles at the tips? (assuming a triangle ascribed by the hands)
* math Puzzler.. - Ken, Thursday, November 16, 2006 at 12:50pm
Of course, the hands never actually move "toward each other" as they are travleing in the same direction,(yes?) but the speed of aproach and recession for he points of the hands does, and is a great question. :)
* math Puzzler.. - quizzical, Thursday, November 16, 2006 at 6:04pm
Bob: the first thing that jumped out at me when you said 5 was the 3-4-5 triangle being involved and it is almost a 'trick' question... with no difficult forumulas needed. I'll think on that, thanks for the hint
Lance: the size of the clock face itself wouldn't matter because what we are after is the relationship between the two hands (the lengths of which we are given).
Ken: Theats right. they are always moving in the same direction.. I was thinking rates of change, but I had no function to start with so I didn't know where to start :(
Thanks for the responses everyone...
Assume the clock hands are phasors. Maximum apparent frequency occurs when the displacements are ninety degrees. Frequency on the phasor plot relates to velocity on postion, time plot.
This is a very old planetary problem, originally laid out on the astrolabe. Apparent planet veloicty was always maximum when the moving planet was halfway in angular rotation between the minimum and maximum distance from the reference planet.
Analytically, this problem is a mess. It probably is easier to simulate than to solve.