(SO WHAT GOES WHERE?!) 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 about the same amount of time, about 2.2 seconds. Use the pendulum formula below to find out how long the swing is. Round your answer to the tenths place. (equation and answers attached)

Question

anonymous · Answer

Does the 2.2 replace 'T'?

anonymous · Answer

@mathstudent55 Don't mean to bug you, but yeah... >.< .. I've been working on this quiz alone pretty much all day, but I always get this one wrong cuz I'm not really sure where the 2.2 goes an how to get rid of the fraction under the radical (do I use the rationalizing the denominator rule or... o_o)

mathstudent55 · Answer

Here is the formula.

$T = 2 \pi\sqrt{\frac{L}{32} }$

Plug in 2.2 for T, the time, and solve for L.

matt101 · Answer

Yes, the 2.2 replaces the T. The T in the equation is the period, the length of time it takes to complete one cycle of whatever you're looking at (in this case the how long it takes for one swing).:

$$T=2 \pi \sqrt{\frac{ L }{ 32 }}$$
$$2.2=2 \pi \sqrt{\frac{ L }{ 32 }}$$
$$0.35=\sqrt{\frac{ L }{ 32 }}$$
$$0.12=\frac{ L }{ 32 }$$
$$L=3.84$$
Your answer would be D.

matt101 · Answer

Also keep in mind the 32 in the equation is the acceleration due to gravity, 32 ft/s^2.

anonymous · Answer

okay so the 0.35 is from what? squaring it to get rid of the square root?

matt101 · Answer

2.2/2pi = 0.35

0.35^2 = 0.12

anonymous · Answer

OOHHHHH MY GOD NOW I GET IT.

mathstudent55 · Answer

$T = 2 \pi\sqrt{\frac{L}{32} }$

$2.2 = 2 \pi\sqrt{\frac{L}{32} }$

Divide both sides by $2\pi$

$\dfrac{2.2}{2 \pi} = \sqrt{\frac{L}{32} }$

Square both sides:

$\left( \dfrac{2.2}{2 \pi} \right)^2 = \dfrac{L}{32} $

Multiply both sides by 32:

$32\left( \dfrac{2.2}{2 \pi} \right)^2 = L $

$L = 32\left( \dfrac{2.2}{2 \pi} \right)^2$

Now use your calculator.

$L = 3.923156...$

or rounded off as

$L = 3.9$

anonymous · Answer

FINALLY THIS DUMB pellet MAKES SENSE. THANK YOU BOTH SO MUCH. 
I'd give both of you those silly medal things but yeah... I can't. Dumb glitch in the site. But really, thank you thank you thank you!

mathstudent55 · Answer

You're welcome. I'm glad you understand it now.