Question

The period p of a pendulum, or the time it takes the pendulum to make one complete swing, varies directly as the square root of the length L of the pendu- lum. If the period of a pendulum is 1.5 s when the length is 2 ft, find the period when the length is 5 ft. Round to the nearest hundredth

Answer 1

What do you think the answer is? :)
State your process.

Answer 2

@Vickyisthesmartone123 at least show OP how to start the problem.

Answer 3

Okay, so I was thinking that 2/1.5=1.33

Answer 4

1.33*5=6.7

Answer 5

have you studied "direct variation" ?

Answer 6

Not familiar with the tem

Answer 7

*term

Answer 8

I suspect you (should!) have learned it.

the simple equation if y directly varies with x is

y = k x
where k is some constant (which in these problems you have to first find)

your problem is a bit more complicated, because
p varies directly with the square root of L

which , as an equation means
\[ p= k \sqrt{L} \]

Answer 9

eeek that sounds complicated o_O

Answer 10

the steps are to use the first part of the info
If the period of a pendulum is 1.5 s when the length is 2 ft
to find what "k' is

then once you know k, you use it and the other info
the length is 5 ft.

to find the period

Answer 11

you can give it a try.

you start with
\[ p = k \sqrt{L}\]

now look at the info
the period of a pendulum is 1.5 s when the length is 2 ft

what number should we use for p and what number for L ?

Answer 12

The p is 1.5 and the L is 2?

Answer 13

yes. if you use those numbers instead of the letters in the "variation equation"
\[ p = k \sqrt{L} \]
what do you get ? i.e. what is the equation with numbers instead of letters?

Answer 14

1.5 = k sqroot of 2

Answer 15

do you know how to "solve for k" ?

Answer 16

you should divide both sides by sqr(2)

Answer 17

Hmm... no idea, but I think k=1.06?

Answer 18

Aww darn I just found out that my mom says I gtg, I am so so sorry, but than you for helping me set up the problem, I will try to figure out the rest of it later. thank you so much for teaching me the concept up to this point!!

Answer 19

\[ \sqrt{2}k= 1.5\\
\frac{\sqrt{2}}{\sqrt{2}}k= \frac{1.5}{\sqrt{2}} \\
k= \frac{1.5}{\sqrt{2}}
\]

yes k=1.06, but because they want the answer to the nearest 100th
I would keep more digits
k= 1.06066

Answer 20

Oh okay cool, wait so 1.06 is the final answer? that's all the steps to solve the problem?

Answer 21

now you put in 1.06066 for k
and 5 for L
and do the math, to find p

Answer 22

Alright, thank you Phi!! and I am sorry for cutting it short, will use the concept to figure it out later!