Question

A pendulum is 18 feet long. It's central angle is 44°. The pendulum makes one back and forth swing every 12 seconds. To the nearest foot, how far does the pendulum swing each minute

Answer 1

Answer: it swings 138 feet in 1 minute

Step-by-step explanation:

The back and forth movement of the pendulum represents the length of the arc of the circle.

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = length of pendulum = 18 feet

θ = 44°

Length of arc = distance moved by the pendulum in one direction.

Therefore,

Length of arc = 44/360 × 2 × 3.14 × 18

Length of arc = 13.816 feet

The pendulum makes one back and forth swing every 12 seconds. It means that the distance it covers in one back and forth movement is

13.816 × 2 = 27.632 feet

If the pendulum swings 27.632 feet in 12 seconds, then

In 60 seconds(1 minute), the distance covered would be

(60 × 27.632)/12 = 138 feet