Question

the period t (in seconds) of a pendulum is given by $t = 2pisqrt{\frac{l}{32}}$, where l stands for the length (in feet) of the pendulum. if $pi = 3.14$, and the period is 1.57 seconds, what is the length?
20 feet
2 feet
16 feet
8 feet

Explanation:

Step1: Substitute given values into formula

Given $T = 1.57$, $\pi=3.14$, and $T = 2\pi\sqrt{\frac{L}{32}}$. Substitute to get $1.57=2\times3.14\sqrt{\frac{L}{32}}$.

Step2: Simplify the right - hand side coefficient

$2\times3.14 = 6.28$, so the equation becomes $1.57 = 6.28\sqrt{\frac{L}{32}}$.

Step3: Solve for $\sqrt{\frac{L}{32}}$

Divide both sides of the equation by $6.28$: $\sqrt{\frac{L}{32}}=\frac{1.57}{6.28}=\frac{1}{4}$.

Step4: Square both sides

$(\sqrt{\frac{L}{32}})^2 = (\frac{1}{4})^2$, which gives $\frac{L}{32}=\frac{1}{16}$.

Step5: Solve for $L$

Cross - multiply: $16L = 32$, then $L = 2$.

Answer:

2 feet