Answer:
Length L = 51.88 feet
Step-by-step explanation:
From the given information,
The length of the pendulum can be determined by using the Formula for the period T which is the time of one full oscillation of a simple pendulum.
[tex]T = 2 \pi \sqrt {\dfrac{L}{g}}[/tex]
where;
T = period of the time of one full oscillation = 8 seconds
L = length in feet
g = acceleration due to gravity in feet = 32 ft/s²
π = 22/7
[tex]8 = 2 \times \dfrac{22}{7} \times \sqrt {\dfrac{L}{32}}[/tex]
[tex]8 = 6.2857 \times \sqrt {\dfrac{L}{32}}[/tex]
[tex]\dfrac{8}{6.2857} =\sqrt {\dfrac{L}{32}}[/tex]
[tex]1.273=\sqrt {\dfrac{L}{32}}[/tex]
[tex]1.273= {\dfrac{\sqrt L}{ \sqrt {32}}}[/tex]
[tex]1.273 \times { \sqrt {32}}}= {\sqrt L}[/tex]
[tex]7.2012= {\sqrt L}[/tex]
L = 7.2012²
L = 51.88 feet
