perplexus.info :: Geometry : Like Clockwork

Like Clockwork (Posted on 2004-02-27)

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: 3.7000 (10 votes)

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calculus based solution

| Comment 3 of 36 |

parametrize the two curves

4cos(60t) i +4sin(60t)j sub in Ai +BJ

3cos(t)i +3sin(t)j sub in Ci+Dj

note minute hand moves 60 times faster than hour hand

distance = sqrt( (A-C)^2+ (B-D)^2 )

want to maximize first derivative so set second derivative equal to zero!!!

Posted by red_sox_fan_032003 on 2004-02-27 14:56:31

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