Variation Functions word problem

Printable View

December 31st 2010, 09:11 AM
stuckonmath

Variation Functions word problem

Hi, I have a couple word problems that I have to do for homework and I am stuck on one of them.

When you swim underwater, the pressure in your ears varies directly with the depth at which you swim. At 10 feet, the pressure is about 4.3 pounds per square in, (psi). Write the particular equation expressing pressure in terms of depth.

I think that the general equation is p = kx but I'm not sure how to relate that to the problem. I would appreciate any help. Thanks!
December 31st 2010, 09:21 AM
janvdl

Quote:

Originally Posted by stuckonmath

Hi, I have a couple word problems that I have to do for homework and I am stuck on one of them.

When you swim underwater, the pressure in your ears varies directly with the depth at which you swim. At 10 feet, the pressure is about 4.3 pounds per square in, (psi). Write the particular equation expressing pressure in terms of depth.

I think that the general equation is p = kx but I'm not sure how to relate that to the problem. I would appreciate any help. Thanks!

Yes you have the right idea. If something is directly proportional, the formula is given by the proportionality statement times some constant $k$ .

So if the depth at 10 feet is 4.3 psi, then at 1 foot it is 0.43 psi.

What should your equation $P = d \times k$ look like then?
(d is the depth, and k the constant increase in psi per foot.)
December 31st 2010, 09:29 AM
stuckonmath

1 = 4.3x?
December 31st 2010, 09:38 AM
e^(i*pi)

If you use the information in the question you would go with $P = kh$ where h is depth and k some constant. The question is asking you to find P in terms of h which is the same as finding the constant k.

To find k sub the information given in the question to find the constant (but first convert your depth to inches for unit consistency): $k = \dfrac{P}{h} = \dfrac{4.3}{120} (lb \cdot in}^{-3})$
December 31st 2010, 09:45 AM
janvdl

Quote:

Originally Posted by e^(i*pi)

To find k sub the information given in the question to find the constant (but first convert your depth to inches for unit consistency): $k = \dfrac{P}{h} = \dfrac{4.3}{120} \text{lb \cdot in}^{-3}$

Sorry, I'm not quite sure why you're using 120 and not 10? A typo?

EDIT: Nevermind, I see you converted.
December 31st 2010, 09:46 AM
stuckonmath

I don't think it's soposed to be that complicated and I don't understand how you got there.
December 31st 2010, 09:50 AM
janvdl

Quote:

Originally Posted by stuckonmath

I don't think it's soposed to be that complicated and I don't understand how you got there.

I think perhaps e^(i*pi) is overestimating your knowledge of the subject.

However he gives you a good clue in finding the constant.

$k = \frac{P}{d} = \frac{4.3}{10} = ?$

Then you simply substitute that constant into:

$P = d \times k$
December 31st 2010, 09:51 AM
e^(i*pi)

Quote:

Originally Posted by janvdl

Sorry, I'm not quite sure why you're using 120 and not 10? A typo?

EDIT: Nevermind, I see you converted.

The LaTeX on the units didn't render

Quote:

Originally Posted by stuckonmath

I don't think it's soposed to be that complicated and I don't understand how you got there.

I took out the first part because, on reflection, it doesn't really matter to this question

Using the equation that you said in the OP (P = kx) and the data you're given in the question I derived an equation to find the constant of proportionality k. You need to find the value of k because it asks for an expression of P in terms of x
December 31st 2010, 10:07 AM
stuckonmath

so is it 4.3 = 10k?
December 31st 2010, 10:46 AM
e^(i*pi)

I would change your depth into inches in order to be consistent with your pressure being pounds per square inch but that would work although it would give units of lb·in^-2·ft^-1

4.3=120k would be lb·in^-3