Question

3 multiple choice 20 points tommy visited the museum of history and technology with his class. they saw foucaults pendulum in pendulum hall. he knew from science class that the time it takes a pendulum to complete a full cycle or swing depends upon the length of the pendulum. the formula is given by (t = 2pisqrt{\frac{l}{32}}) t represents the time in seconds and l represents the length of the pendulum in feet. he timed the swing of the pendulum with his watch and found that it took about 8 seconds for the pendulum to complete a full cycle. what is the length of the pendulum in feet rounded to the nearest whole number? 53 feet 52 feet 42 feet 51 feet 4 multiple choice 10 points

Explanation:

Step1: Substitute given value of T

Given $T = 8$, substitute into formula $T=2\pi\sqrt{\frac{L}{32}}$, we get $8 = 2\pi\sqrt{\frac{L}{32}}$.

Step2: Isolate the square - root term

First, divide both sides by $2\pi$. $\frac{8}{2\pi}=\sqrt{\frac{L}{32}}$. Since $\frac{8}{2\pi}=\frac{4}{\pi}\approx\frac{4}{3.14}\approx1.27$. So $1.27=\sqrt{\frac{L}{32}}$.

Step3: Square both sides

$(1.27)^2=\frac{L}{32}$. Then $L = 32\times(1.27)^2$.

Step4: Calculate the value of L

$L=32\times1.6129 = 51.6128\approx52$.

Answer:

52 feet