trig

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 to the nearest foot.)

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  1. s = rθ = 18(44*pi/180) = 13.82ft in one arc

    It makes 10 (5 back and forth) swings every minute.

    Total travel: 138 ft

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  2. s=rØ r=18 Ø= (11π/45) radians
    s=18(11π/45)
    s≈13.82 ft/sec

    60sec÷12sec= 5sec
    5×2=10
    10×13.82=138.2

    The pendulum travels 138 feet each minute

    Degrees to radians;

    (44÷1) × (π÷180) = (11π÷45)

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  3. we all get the same answer but I like mine:
    The central angle is 44 degrees or 44/360= .122 th of the entire circle. Call the length of the arc associated with the central angle, x. Since the length of the pendulum is 18 ft. the circumference of the implied circle is cir=2 pi (18)
    = 36 pi ft.. By the nature of central angle to total we know
    44 degrees /360 degrees = x ft. / 36 pi ft. or
    x= 13.8 ft.
    As mentioned above one full swing is 2x feet or in one minute
    10 x = 10 (13.8 ft) = 138 ft.

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