Question

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?

Answer 1

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`.