The hands of a clock in some tower are approximately 2m and 1.5m in length. How fast is the distance between the tips of the hands changing at 9:00?

1 Answer
Apr 29, 2015

It is possible to assume that the two hands are vectors and the center of the clock is the origin of two cartesian axes. The minute hand is a vector whose lenght is #2m,# and its angle is #90°#. The hour hand is a vector whose lenght is #1.5m#, and its angle is #180°#.

The two vectors, in cartesian coordinates can be written:

#vecm(0,2)#

#vech(-1.5,0)#

The distance from the tips is easily:

#d=sqrt(2^2+1.5^2)=sqrt(4+2.25)=sqrt6.25=2.5m#.