Question

If you use spray-on deodorant, you can find out how fast it comes out of the can if you know the relative pressure inside the can. Supposing a full can of deodorant has an exit velocity (v) of 42 feet per second, use the formula below to find the relative pressure inside the can (p) in psi (pounds per square inch): (photo attached)

Answer 1

What I did:
\[v =7 \sqrt{p} \]\[42^2 = 7\sqrt{p}^2\]\[1764 = 7p\]\[252 = p\]

Answer 2

Are you sure you're using the right versions of measurements. I'm European so we use the SI metric system. Anyhow, whatver you use, must be of the same type of measurement. I know that feet isn't the same as inch. So you'll have to do a conversion.

Why did you square the velocity?

Answer 3

Convert the 42 feet/s to inch/s.

Ok, I see why you squared everything: to get rid of the squareroot.

Answer 4

Yeah. I squared to get rid of the square root. xD

Answer 5

You forgot to square the 7, too.

Answer 6

But you forgot to square the 7 as well. If you square the velocity, you must also square 7 and the root.

Answer 7

E.g.:
\[
v=7\sqrt{p}
\]Squaring both sides:
\[
\frac{v^2}{49}=p
\]

Answer 8

When I re did the problem (with squaring the 7) I got 36

Answer 9

And apparently there's no need to convert from feet to inch... weird. Wrong problem.

Answer 10

It's weird... this programme is weird. I don't even like it tbh. But did everyone else get 36 xD haha

Answer 11

If this is homework make a note of it to the teacher that the problem forget that feet isn't inch.

Answer 12

I'll tell her that tomorrow when I see her.

Answer 13

*forgot or forgets

Answer 14

\[
\left(\frac{42}{7}\right)^2=6^2=36
\]
As for the conversion. It seems that the proportionality constant of 7 takes care of that.

Answer 15

I thought 1 foot was 12 inches.

Answer 16

Remember that pressure is \(F/A\). So, it includes some other stuff there, too, not just feet to in.

Answer 17

yeah ok. Maybe it's because I'm not really familiar with these type of lengths and weights and its conversions. I had to look it up. Metric is more straightforward.

Answer 18

Completely agree.