Question

Assuming that the hour hand on an analog clock does not move with the minute hand (in a real clock, it does), what is the arc length between the hour hand and minute hand of an analog clock at 10:10? State your answer in terms of r since we do not know the radius. Why might this be a common time for clock makers to use for images of their clocks?

Answer 1

Given the hour-hand and minute hand of an analog clock:

Length of an arc =

`l=(\theta)/(360)*2\pi r`

where

r = radius

pi = 3.142

`\begin{gathered} l=(\theta)/(360)*2\pi r \\ l=(120)/(360)*2*3.142* r \\ l=2.095r \end{gathered}`

Hence the arc length = 2.095r

Therefore the correct answer is 2.095r