At noon, ship A is 130 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM? This is kinda confusing...need help please!!!

- anonymous

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- Babynini

What..college do you go to by chance? xD I legit just did this question!

- anonymous

Really? University actually!

- Babynini

Calc 1?

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## More answers

- Babynini

Bah unoriginal problem-writers! xP

- anonymous

yope

- Babynini

oh how fuun o.o

- anonymous

yh yh...not so fun!

- anonymous

what's confusing is the 4pm..not sure how to go about that

- Babynini

Righto. let me look through all my scratch paper to try and find it lol.
You multiply the x and the y by 4 eventually. since the time form noon to four is four hours.

- Babynini

Have you tried drawing it out? :)

- anonymous

lol...okay...yeah, I did...just wasn't sure of the time like would it be from 12am or 12noon?

- Babynini

12 noon, for sure.

- Babynini

K, so still need help?

- Babynini

|dw:1446619451979:dw|
so this is sort of how I drew it xD

- Babynini

all make sense thus far?

- anonymous

yeah, similar to my drawing...lol...please do go on!

- anonymous

oh my goodness, the question said at noon...lol...didn't see that

- Babynini

gorgeous, gorgeous.
Ok so from that we can get the simple triangle|dw:1446619724508:dw|

- Babynini

it's ok, we've all been there haha
does that all make sense?! I got confused at that part in class so don't hesitate to ask questions!

- Babynini

|dw:1446619924579:dw|

- Babynini

for now we don't really care about z, so no worries about finding it

- anonymous

yeah, it makes sense...is making sense

- Babynini

is it..is it reaaally?

- anonymous

wait, the 30km/h dosn't necessarily have to be negative does it?

- Babynini

It does because the space is getting smaller and getting smaller means negative.
I mean, the space between the ships is getting smaller and A is approaching B which is why the A if negative and not the B.

- Babynini

haha sorry if that was more confusing xD make sense, sort of?

- anonymous

ummm, yeah...sort of

- Babynini

|dw:1446620270925:dw|

- anonymous

okay...I get

- Babynini

...ok haha. Sorry, idk how to explain it better :/ Anyway.
Thats all at noon and we care about what happens between then and 4
So we need another triangle!
Since from noon to 4 = 4 hours, we're going to take the numbers from the last triangle and multiply each side by 4

- Babynini

so
x = -30
y = 20
multiply those each by 4

- anonymous

okay..so what I did was sum both and multiply sum by 4...totally wrong I'm guessing?

- Babynini

You're looking for 2 different sides, so you won't want to add them :)
just
x = -30*4 = ?
y = 20*4 = ?

- anonymous

yeah...right!...-120 and 80

- Babynini

make sense?
Ok so y is pretty straight forward, for x though we want to subtract 120 from 130 (the distance from A to B
so
130-120= ?

- Babynini

|dw:1446620783497:dw|

- Babynini

|dw:1446620869735:dw|

- Babynini

Does that work for you? :)

- Babynini

And all that was from the ORIGINAL
Because the speed of B = 20km/h
and the speed of A = 30km/h

- anonymous

okay...the question says how fast is the distance between the ships changing...that suggests one answer...so if A is changing at 10km/h and B is changing at 80km/h then...

- anonymous

wait!...when we subtracted 120 from 130 we ignored the minus sign?

- Babynini

it's 130+(-120) so we're fine :)

- Babynini

sorry, I just skipped over that. Thanks for correcting me!

- Babynini

ok, the end is near xD
from that last triangle with x = 10 and y =80 can you find z for me, please?

- anonymous

SQRT 6500

- Babynini

Perfect.
And using that Pythagorean theorem again we can find our dy/dt!!

- Babynini

x^2 +y^2 = z^2
can you find the derivative of that?

- anonymous

2x+2ydy/dt=2z?

- anonymous

or nah!

- Babynini

super close. These always mess me up too.
2x(dx/dt)+2y(dy/dt)=2z(dy/dt)

- Babynini

notice anything we can factor out?

- anonymous

oh okay...divide through by 2?

- Babynini

absolutely!! and we end up with?

- Babynini

[I would go over getting that derivative later on your own, I would explain more but I gotta go to bed soon lol, just to make sure you understand it because it is confusing :/]

- anonymous

yeah sure...thanks for your time really

- Babynini

np. After you factor out 2 you end up with...

- anonymous

xdx/dt+ydy/dt=zdy/dt...and then we isolate dy/dt..or at least take like terms to one side?

- Babynini

Perfect! yeah we want to isolate dy/dt so we would end up with
[x(dx/dt)+y(dy/dt)]/z = dy/dt
yeah?

- Babynini

gah! the one by y should e z should be (dz/dt) and we're looking for dz/dt not dy/dt

- Babynini

so [x(dx/dt)+y(dy/dt)]/z = dz/dt
sorry about that :)

- anonymous

right

- Babynini

so our values we know are
x=
y=
z=
dx/dt=
dy/dt=
Can you fill those in? :)

- Babynini

for z, y, x look at the last triangle we drew. Where z was a square root..

- anonymous

x=10,y=80,z=SQRT6500

- anonymous

dx/dt=30?

- Babynini

don't forget the negative. But yes!

- anonymous

dy/dt=20?

- Babynini

exactly. So now you take those numbers and plug them all in and solve for dy/dt!

- anonymous

dz/dt

- Babynini

\[\frac{ (10(-30))+80(20) }{ \sqrt{6500}} = \frac{ dy }{ dt }\]

- Babynini

agaihg idk why I keep saying dy. Yeah you're right.

- Babynini

Then simplify the square root and all that fun stuff. You got it from here? :)

- anonymous

yeah...absolutely!...thank you so much for your time!!!

- Babynini

Of course! Good luck man :) Hopefully this will help me remember how to do it too xD

- Babynini

http://www.mathwarehouse.com/arithmetic/square-root-calculator.php ...just in case you're not good at simplifying sq roots. I suck at it xD

- anonymous

lol...Okay!...thanks man!...do have a good night!

- anonymous

thanks a bunch :-D

- Babynini

no problem :)

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