Question

Once a week you babysit your neighbor’s toddler after school, usually going to a local playground. You notice that each swing on the swing set takes nearly the same amount of time, about 2.7 seconds. Use the pendulum formula below to find out how long the swing is. Round your answer to the tenths place. A.37 feetB.5.4 feetC.1.8 feetD.5.9 feet

Answer 1

Explanation

We are given the following pendulum formula:

`\begin{gathered} T=2\pi\sqrt{(L)/(32)} \\ where \\ T=timetaken \\ L=Length \end{gathered}`

We are required to determine the length of the swing.

This is achieved thus:

`\begin{gathered} T=2\pi\sqrt{(L)/(32)} \\ where \\ T=2.7seconds \\ \\ \therefore2.7=2\pi\sqrt{(L)/(32)} \\ \text{ Divide both sides by }2\pi \\ (2.7)/(2\pi)=\frac{2\pi\sqrt{(L)/(32)}}{2\pi} \\ (2.7)/(2\pi)=\sqrt{(L)/(32)} \\ \text{ Square both sides } \\ ((2.7)/(2\pi))^2=(\sqrt{(L)/(32)})^2 \\ ((2.7)/(2\pi))^2=(L)/(32) \\ (L)/(32)=(2.7^2)/(4\pi^2) \\ \\ \therefore L=(2.7^2*32)/(4\pi^2) \\ L\approx5.9\text{ }feet \end{gathered}`

Hence, the answer is:

`L\approx5.9\text{ }feet`

Option D is correct.