Question

A pendulum is 18 feet long. Its central angle is 44º. The pendulum makes one back and forth swing every 12 seconds. Each minute, the pendulum swings _____ feet.

Answer 1

Radius: r=18 feet
Cental Angle: A=44°
Each cycle (one back and forth) lasts 12 seconds
In each cycle the pendulum swings:
L=(A/360°) 2 pi r
L=(44°/360°)(2)(3.141592654)(18 feet)
L=(0.122222222)(113.0973355 feet)
L=13.82300764 feet
Rounded to 3 decimal places:
L=13.823 feet

Each minute (60 seconds) the pendulum makes:
Number of cycles: n=(60 seconds) / (12 seconds)→n=5 cycles

Then, each minute, the pendulum swings:
T=nL=5(13.823 feet)→T=69.115 feet

Answer: Each minute, the pendulum swings 69.115 feet.