Question

Arc Length: The pendulum on a grandfather clock swings from side to side once every second. If the length of the pendulum is 4 feet and the angle through which it swings is 20 degrees, how far does the tip of the pendulum travel in 1 second?

Answer 1

Imagine the path of the tip of the pendulum as an arc of a circle. The circle would have a radius of 4 feet and the arc would be 20 degrees. To calculate the length of the arc, you need to find 20 degrees of the circumference. 

Length of Arc = 2*pi*R*Degree of arc/360 
Length of Arc = 2*pi*4*20/360 
Length of Arc = 8pi * 1/18 
Length of Arc = 4/9 pi feet 
Length of Arc ~ 1.396263402 feet 

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