Question

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below.

Answer 1

46.08 ft

doesn't feel right but if you plug it in it works

2.4pi=2pi(46.08/32)^1/2

Answer 2

we are given

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation as

$f(l)=2\pi \sqrt{\frac{l}{32} }$

where l is the length of the pendulum in feet

We have

$f(l)=2.4\pi$

so, we can set them equal and then we can solve for l

$2.4\pi=2\pi \sqrt{\frac{l}{32} }$

Firstly, we will take square both sides

$\left(2.4\pi \right)^2=\left(2\pi \sqrt{\frac{l}{32}}\right)^2$

$\frac{\pi ^2l}{8}\cdot \:100=5.76\pi ^2\cdot \:100$

$\frac{25\pi ^2l}{2}=576\pi ^2$

$\frac{2\cdot \:25\pi ^2l}{2}=2\cdot \:576\pi ^2$

$25\pi ^2l=1152\pi ^2$

$\frac{25\pi ^2l}{25\pi ^2}=\frac{1152\pi ^2}{25\pi ^2}$

$l=\frac{1152}{25}$

$l=46.08feet$

So,

The length of a pendulum that takes 2.4 pi seconds to swing back and forth is 46.08 feet..........Answer