the pendulum on a grandfather clock swings from side to side once every second. If the length of the pendulum is 3 feet and the angle through which it swings is 10 degrees, how far does the tip of the pendulum travel in 1 second?

check the picture below

thus [tex]\bf s=\cfrac{r\theta\pi }{180}\qquad \begin{cases} s=\textit{arc's length}\\ r=radius\\ \theta=\textit{angle in degrees}\\ ----------\\ r=3\\ \theta=10 \end{cases}\implies s=\cfrac{3\cdot 10\cdot \pi }{180}[/tex]

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boffeemadrid boffeemadrid · Answer 2 · 2021-10-02T11:24:26+02:00

We need to find the distance the tip of the pendulum travels in one second.

The tip of the pendulum travels 0.52 feet in 1 second.

The length of the pendulum is 3 feet which is the radius (r).

The angle of the swing is [tex]10^{\circ}[/tex] which is [tex]\theta[/tex].

The time given is 1 second.

The distance the tip of the pendulum will travel in one second will be the arc length of the sector of the circle.

The formula to find arc length is

[tex]s=\dfrac{r\theta\pi}{180}\\\Rightarrow s=\dfrac{3\times 10\times\pi}{180}\\\Rightarrow s=0.52\ \text{feet}[/tex]

The tip of the pendulum travels 0.52 feet in 1 second.

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