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?
(In reply to
why calculus by Axorion)
Dan Porter, sorry to burst your bubble, however, there is not a uniform change in the angle. This is due to the fact that the minute hand and the hour hand move at different rates. Do not neglect the fact that the hour hand is still moving, just much less. The easiest way to set up this problem is by using parametric equations to represent the motion of each of the hands. The distance between the two hands is the difference of these two equations. Then, find the fastest rate of change in the distance. For this time, find the distances between the two hands (x and y coordinates), and use pathagoreon's theorem to solve for the distance.

Posted by Steve
on 20040303 19:02:54 