Answer:
3.9 units
Step-by-step explanation:
We are given that,
Time taken by each swing = 2.2 seconds
The pendulum formula is given by, [tex]T = 2\pi \sqrt{\frac{L}{32}}[/tex], where T is the time taken and L is the length of the swing.
So, we have,
[tex]2.2= 2\pi \sqrt{\frac{L}{32}}[/tex]
i.e. [tex]\frac{2.2}{2\pi}=\sqrt{\frac{L}{32}}[/tex]
i.e. [tex](\frac{2.2}{2\pi})^{2}=\frac{L}{32}[/tex]
i.e. [tex]L=32\times (\frac{2.2}{2\pi})^{2}[/tex]
i.e. [tex]L=32\times \frac{4.84}{4 \pi^2}[/tex]
i.e. [tex]L=32\times \frac{1.21}{\pi^2}[/tex]
i.e. [tex]L=\frac{38.72}{9.87}[/tex]
i.e. L = 3.923 units
So, rounded to tenths, the length of the swing is 3.9 units.
