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.)
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
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)
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.
Well, that pendulum sure knows how to swing its way into my heart! Let's do some math-juggling here:
We have a central angle of 44º in a circle, which means the pendulum swings back and forth for 44º. Since a complete circle is 360º, we can determine that the pendulum swings for 44/360 or 0.1222 of a full circle.
Now, we know that the pendulum makes one back and forth swing every 12 seconds. In other words, it completes one full swing in 12 seconds. So, each full swing represents 0.1222 portion of the 18 feet pendulum.
To find out how much the pendulum swings in one minute, we need to find the number of full swings that occur in 60 seconds (1 minute). Since each swing takes 12 seconds, we can do some quick division: 60 seconds / 12 seconds = 5 full swings.
Multiplying the number of full swings (5) by each full swing's portion of the 18 feet pendulum, we get: 5 * 0.1222 * 18 = 11.016 feet.
Rounding it to the nearest foot, we have that the pendulum swings approximately 11 feet each minute. Isn't that a swinging good time?
To find the number of feet the pendulum swings in one minute, we need to determine the total distance covered by the pendulum in one back and forth swing.
Since the pendulum makes one back and forth swing every 12 seconds, we can define a complete swing as the distance it covers from one extreme point to the other and back to the initial point. This distance is equal to twice the length of the pendulum.
Given that the length of the pendulum is 18 feet, the total distance covered in one complete swing is:
2 * 18 = 36 feet.
Next, we need to determine the number of swings the pendulum makes in one minute. There are 60 seconds in a minute, and the pendulum takes 12 seconds for each swing. Thus, the number of swings in one minute is:
60 seconds per minute / 12 seconds per swing = 5 swings.
Now, to find the total distance covered by the pendulum in one minute, we multiply the distance covered in one swing by the number of swings in one minute:
36 feet per swing * 5 swings per minute = 180 feet per minute.
Therefore, the pendulum swings approximately 180 feet in one minute.