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
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.

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

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

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

$$\displaystyle{x}={r}\theta$$
$$\displaystyle{x}={40}∗{0.3490}={13.96}\ \text{ inches }$$