To determine how long it takes for a pendulum of length [tex]\( L = 4.84 \)[/tex] meters to swing back and forth once, we use the formula:
[tex]\[ t = 2.01 \sqrt{L} \][/tex]
Here, [tex]\( L = 4.84 \)[/tex] meters. Let's calculate the time step-by-step:
1. Substitute the length of the pendulum into the formula:
[tex]\[ t = 2.01 \sqrt{4.84} \][/tex]
2. Calculate the square root of 4.84:
[tex]\[ \sqrt{4.84} \approx 2.2 \][/tex]
3. Multiply this result by 2.01:
[tex]\[ t \approx 2.01 \times 2.2 = 4.422 \][/tex]
Now, let's round this result to the nearest tenth. To do this, we look at the first digit after the decimal point:
[tex]\[ 4.422 \][/tex]
The first digit after the decimal point is 4. Since it is less than 5, we round down. Therefore, the rounded value of [tex]\( t \)[/tex] to the nearest tenth is:
[tex]\[ t \approx 4.4 \][/tex]
Thus, it takes approximately [tex]\( 4.4 \)[/tex] seconds for the pendulum to swing back and forth once when its length is 4.84 meters.
