# Finding closest distance

1. Jan 16, 2007

### thomasrules

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. 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

2. Jan 16, 2007

### Dick

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

3. Jan 16, 2007

### thomasrules

sorry i'm lost

4. Jan 16, 2007

### HallsofIvy

Staff Emeritus
"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?

5. Jan 17, 2007

### thomasrules

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

Last edited: Jan 17, 2007
6. Jan 17, 2007

### Dick

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.

7. Jan 17, 2007

### thomasrules

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

8. Jan 17, 2007

### arildno

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?

Last edited: Jan 17, 2007
9. Jan 17, 2007

### Dick

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

10. Jan 17, 2007

### thomasrules

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

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

11. Jan 17, 2007

### arildno

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?

12. Jan 17, 2007

### thomasrules

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)

13. Jan 17, 2007

### arildno

Is (3.53-8*0,0)=(0,0)?? ?

14. Jan 17, 2007

### thomasrules

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

15. Jan 17, 2007

### thomasrules

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

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

16. Jan 17, 2007

### Dick

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

17. Jan 17, 2007

### thomasrules

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

I did derivative. Set it to 0. Got 0.7

Thats not the answer

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

18. Jan 17, 2007

### Dick

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

19. Jan 17, 2007

### thomasrules

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)

20. Jan 17, 2007

### Dick

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