Question

Movement of a Pendulum A pendulum swings through an angle of 20∘ each second. If the pendulum is 40 inches long, how far does its tip move each second? Round answers to two decimal places.

Trigonometric equation and identitie
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asked 2021-03-04
Movement of a Pendulum A pendulum swings through an angle of 20∘ each second. If the pendulum is 40 inches long, how far does its tip move each second? Round answers to two decimal places.

Expert Answers (1)

2021-03-05

Length of pendulum (r)=40inches Angle covered due to swinging of pendulum in 1 sec \(\displaystyle{\left(θ\right)}={20}°\)
Distance covered by the pendulum in each second(x)=?
Since pendulum moves in a circle so length of arc will be equal to distance covered by the tip of pendulum in 1sec \(\displaystyle{x}={r}\theta\)
Since \(\theta\) is in degree so we will conver it into radian

\(\displaystyle\text{Radian measure }\ ={\left(\frac{\pi}{{180}}\right)}∗\ \text{ Degree measure}\)

\(\displaystyle\text{Radian measure }\ ={\left(\frac{\pi}{{180}}\right)}∗{20}^{\circ}\)

Radian measure=0.3490

\(\displaystyle{x}={r}\theta\)

\(\displaystyle{x}={40}∗{0.3490}={13.96}\ \text{ inches }\)

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