Hello!
The answer is:
The correct option is B. the string is 3.9 feet long.
Why?
To solve the problem, we need to use the given formula, substituting "T" equal to 2.2 seconds, and then, isolating "L".
Also, we need to remember the formula to calculate a simple pendulum:
[tex]T=2\pi \sqrt{\frac{L}{g} }[/tex]
Where,
T, is the period in seconds
L, is the longitud in meters or feet
g, is the acceleration of the gravity wich is equal to:
[tex]g=9.81\frac{m}{s^{2} }[/tex]
or
[tex]g=32\frac{feet}{s^{2} }[/tex]
We are given the formula:
[tex]T=2\pi \sqrt{\frac{L}{32} }[/tex]
Where,
T, is the period of the pendulum (in seconds).
L, is the length of the string.
32, is the acceleration of the gravity in feet.
So, substituting "T" and isolating "L", we have:
[tex]2.2seconds=2\pi \sqrt{\frac{L}{32\frac{feet}{seconds^{2}} }}\\\\2\pi \sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}}=2.2seconds\\\\\sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}}=\frac{2.2seconds}{2\pi }[/tex]
Then, squaring both sides of the equation, to cancel the square root, we have:
[tex]\sqrt{\frac{L}{32\frac{feet}{seconds^{2} }}}=\frac{2.2seconds}{2\pi}\\\\(\sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}})^{2}=(\frac{2.2seconds}{2\pi})^{2}=(0.35seconds)^{2} }\\\\\frac{L}{32\frac{feet}{seconds^{2}}}}=0.123seconds^{2}\\\\L=32\frac{feet}{seconds^{2}}*0.123seconds^{2}\\\\L=3.94feet=3.9feet[/tex]
Hence, we have that the answer is:
B. the string is 3.9 feet long.
Have a nice day!
