Celia is staring at the clock waiting for school to end so that she can go to track practice. She notices that the 5-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle.

Part 1: How many radians does the minute hand move from 1:25 to 1:55? (Hint: Find the number of degrees per minute first.)
Part 2: How far does the tip of the minute hand travel during that time?

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JeanaShupp JeanaShupp · Answer 1 · 2019-01-28T11:23:36+01:00

Answer: a) [tex]\pi\text{ radian}[/tex]

b) 15.7 inches

Step-by-step explanation:

We know that the measure of complete circle is [tex]360^{\circ}[/tex].

Therefore,

[tex]60\ minutes=360^{\circ}\\\Rightarrow\ 1\ minute=\frac{360}{60}=60^{\circ}[/tex]

The minute hand move from 1:25 to 1:55, it means the minute have cover 30 minutes.

Now, 30 minutes=[tex]60\times30=180^{\circ}[/tex]

In radians, 30 minutes=[tex]180^{\circ}\times\frac{\pi}{180^{\circ}}[/tex]

Therefore, 30 minutes= [tex]\pi\ radians[/tex]

Also the length of arc is given by

[tex]l=r\theta[/tex]

Now, for radius r= 5 inch and [tex]\theta=\pi[/tex]

Length traveled by the tip of the minute hand travel during that time=[tex]5\times\pi=5\times3.14=15.7\ inches[/tex]