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Like Clockwork (Posted on 2004-02-27) Difficulty: 4 of 5
A clock's minute hand has length 4 and its hour hand length 3.

What is the distance between the tips at the moment when it is increasing most rapidly?

See The Solution Submitted by DJ    
Rating: 4.0000 (9 votes)

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re(2): why calculus | Comment 24 of 29 |
(In reply to re: why calculus by Steve)

Think of it this way. The rate of both hands is a constant so adding or subtracting them will still be a constant rate. Take a battery operated clock. Remove the second hand. Glue a small block to the minute hand. Glue the block to a piece of glass. Now look through the glass at the clock. The hour hand will be moving counter clockwise at a uniform rate slightly slower than a minute hand normally moves clockwise. The tip of the hour hand will be at a constant speed but changing direction. When the tip of the hour hand is moving directly away from the tip of the minute hand we have our max increase. This is at 90 to the unknown segment or as Tristan put it, the point of tangent of a line through the tip of the minute hand to the circle drawn by the hour hand.

I never took calculus although I can do a bit of it. I have found that many problems can be simplified through geometry, algebra, trigonometry, logic and common sense. Of course it helps that I can count the sides of complex polyhedrons in my head. I'm also an accomplished programmer so if it get over my head I can always do successive approximation. Now if I could only remember that mandatory meeting I was reminded is in five minutes I might go back to school and have a cool job!
Edited on March 3, 2004, 10:54 pm
  Posted by Axorion on 2004-03-03 22:30:56

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