# Finding closest distance

## Homework Statement

Ship A, sailing due east at 8 km/h, sights ship B 5km to the southeast when ship B is sailing due north at 6km/h. How close to each other will the two ships get?

## The Attempt at a Solution

I drew the picture. Ship a distance is 8t and B is 6t

Use the a^2+b^2=c^2

Dick
Homework Helper
Seems to me there are two coordinates of interest here. Hint.

sorry i'm lost

HallsofIvy
Homework Helper

## Homework Statement

Ship A, sailing due east at 8 km/h, sights ship B 5km to the southeast when ship B is sailing due north at 6km/h. How close to each other will the two ships get?

## The Attempt at a Solution

I drew the picture. Ship a distance is 8t and B is 6t

Use the a^2+b^2=c^2

"Ship a distance is 8t and B is 6t" distance from what? Set up a coordinate system, say with A initially at the origin. What are the coordinates of ship A at time t? What are the initial coordinates of ship B? What are the coordinates of ship A at time t? What is the (square of the) distance between those points as a function of t?

ok $$D^2=(-3.53+6t^2)+8t^2 dD/dt=(200t-42.36)/whatever\\0=200t-42.36\\t=0.212\\$$
I plugged that in the distance formula and got a wrong answer

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Dick
Homework Helper
Follow HallsOfIvy's suggest and write down the position of the two ships in xy coordinates as a function of time first. It's difficult to tell where you went wrong from what you post.

yes I have a drawing. I used the sin law to find the distance of the 2 sides.

Coordinates (3.53,0) and (3.53,-3.53)

By the way how do you put spaces in latex coding I tried \\ it didnt work

arildno
Homework Helper
Gold Member
Dearly Missed
Eeh??

Do you even know what coordinates are??

Considered as a function of time, what is ship A's position measured from an origin lying where A was, and sighted B somewhere at t=0?
And, with the same choice of origin, what is B's position as a function of time?

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Dick
Homework Helper
At what time? Where is the time dependence? (Not sure about your latex question, sorry).

yes those are the coordinates.from the origin (0,0) using pythagorean theorem,

i use 5sin45=a=3.53, b=3.53

arildno
Homework Helper
Gold Member
Dearly Missed
1. What choice have you made of positive axes?
2. What was A's position at t=0?
3. What is A's position as a function of time?
4. What is B's position as a function of time?

A's position at t=0 is (0,0)
A's position as a function of time is (3.53-8t,0)
B's position as a function of time is (3.53,-3.53-6t)

arildno
Homework Helper
Gold Member
Dearly Missed
Is (3.53-8*0,0)=(0,0)?? ?

ah crap....
A is (8t,0)

**** or is it
A(8t,0)
B(3.53,-3.53+6t)

My guess is that's right if not I quit school

Dick
Homework Helper
You can stay in school! Now what is D^2 as a function of t?

D^2=(-3.53+6t-0)^2+(3.53-8t)^2

I did derivative. Set it to 0. Got 0.7

I'm suppost to plug time into the D^2 and get the distance correct?

Dick
Homework Helper
You seem to be trying to do the right thing. What is the derivative of D^2?

I got it to be:

After the expansion and derivative

dD/dt=200t-98.84/(the rest here doesn't matter cause i'm setting other side to zero)

Dick
Homework Helper
All seems ok. What is the answer supposed to be?

The ships get 0.707km to each other

btw thanks for all your help so far

Dick
Homework Helper
You're welcome. But that answer only differs from 0.7 because you are rounding off differently.

NO! but we only have found the time man not the distance

Dick
Homework Helper
I got it to be:

After the expansion and derivative

dD/dt=200t-98.84/(the rest here doesn't matter cause i'm setting other side to zero)

You are saying your solution for the TIME is 0.7? That's not what this says.

OMG YOU ARE CORRECT!

Thanks man. I'm slow. What's your paypal how much do I owe you.
:tongue2:

And now I have another similar one i'm struggling with it :S