the formula $t = 2pisqrt{\frac{l}{32}}$ gives the time it takes in seconds, $t$, for a pendulum to make one…

the formula $t = 2pisqrt{\frac{l}{32}}$ gives the time it takes in seconds, $t$, for a pendulum to make one full swing back and forth, where $l$ is the length of the pendulum, in feet. to the nearest foot, what is the length of a pendulum that makes one full swing in 1.9 s? use 3.14 for $pi$.

the formula $t = 2pisqrt{\frac{l}{32}}$ gives the time it takes in seconds, $t$, for a pendulum to make one full swing back and forth, where $l$ is the length of the pendulum, in feet. to the nearest foot, what is the length of a pendulum that makes one full swing in 1.9 s? use 3.14 for $pi$.

Answer

Explanation:

Step1: Substitute given values into formula

Given $T = 1.9$, $\pi=3.14$, and the formula $T = 2\pi\sqrt{\frac{L}{32}}$. So, $1.9=2\times3.14\sqrt{\frac{L}{32}}$.

Step2: Simplify the right - hand side

$2\times3.14 = 6.28$, so the equation becomes $1.9 = 6.28\sqrt{\frac{L}{32}}$.

Step3: Isolate the square - root term

Divide both sides by 6.28: $\frac{1.9}{6.28}=\sqrt{\frac{L}{32}}$. Calculate $\frac{1.9}{6.28}\approx0.3025$. So, $0.3025=\sqrt{\frac{L}{32}}$.

Step4: Square both sides

$(0.3025)^2=\frac{L}{32}$. Calculate $(0.3025)^2 = 0.09150625$. So, $0.09150625=\frac{L}{32}$.

Step5: Solve for L

Multiply both sides by 32: $L=0.09150625\times32$. Calculate $L = 2.928192\approx3$.

Answer:

3