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 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: 4.0000 (9 votes)

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 KISS, keep it simple!!!!!!! | Comment 22 of 29 |
(In reply to re: why calculus by Steve)

In addition to analytical and spreadasheeet methods there is a third one, a “common sense” solution.

Assume that:
-the hour hand A is stationary and rests on 12 o’clock.
-The minute hand B is of the same length as A and, beginning at 12 rotates with the speed Vt.

The distance between tips of A and B, (D) changes at the max rate at t=0, when D is perpendicular to A.

For B>A the above occurs when:
A=cos(a)*B, (a) is the angle between A and B

We have:
D=sin(a)*B
And
D=SQRT(B^2-A^2)

For our example
D=sqrt7
Cos(a)=3/4

QED !!!!!!!!!!!!!!!!!

Note that D is independent of Vt.

I move to post the three solutions.

 Posted by joe on 2004-03-03 20:06:00

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