Question

How long is the second hand to the nearest tenth if it moves 2cm in 15 seconds?

Answer 1

let's recall that a circular clock has 360° and 60 seconds per minute.

the seconds hand does 60 seconds in one go-around, and if it has covered 15 seconds on the clock, that gives us an angle of 90°, 15 is one quarter of 60, so in 15 seconds it has covered one quarter of the full circle or 90°.

we also know it covered 2cm, namely the arc's length on the 15 seconds is 2cm.

`\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =90\\ s=2 \end{cases}\implies 2=\cfrac{(90)\pi r}{180}\implies 2=\cfrac{\pi r}{2} \\\\\\ 4=\pi r\implies \cfrac{4}{\pi }=r\implies 1.27\approx r`