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Finding closest distance

  • #1
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1. 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?


2. Homework 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
 

Answers and Replies

  • #2
Dick
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Seems to me there are two coordinates of interest here. Hint.
 
  • #3
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sorry i'm lost
 
  • #4
HallsofIvy
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1. 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?


2. Homework 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
"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
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ok [tex]D^2=(-3.53+6t^2)+8t^2 dD/dt=(200t-42.36)/whatever\\0=200t-42.36\\t=0.212\\[/tex]
I plugged that in the distance formula and got a wrong answer
 
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  • #6
Dick
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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
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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
arildno
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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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  • #9
Dick
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At what time? Where is the time dependence? (Not sure about your latex question, sorry).
 
  • #10
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yes those are the coordinates.from the origin (0,0) using pythagorean theorem,

i use 5sin45=a=3.53, b=3.53
 
  • #11
arildno
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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
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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
arildno
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Is (3.53-8*0,0)=(0,0)?? :confused:?
 
  • #14
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ah crap....
A is (8t,0)
 
  • #15
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**** or is it
A(8t,0)
B(3.53,-3.53+6t)

My guess is that's right if not I quit school
 
  • #16
Dick
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You can stay in school! Now what is D^2 as a function of t?
 
  • #17
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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
Dick
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You seem to be trying to do the right thing. What is the derivative of D^2?
 
  • #19
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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
Dick
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All seems ok. What is the answer supposed to be?
 
  • #21
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The ships get 0.707km to each other

btw thanks for all your help so far
 
  • #22
Dick
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You're welcome. But that answer only differs from 0.7 because you are rounding off differently.
 
  • #23
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NO! but we only have found the time man not the distance
 
  • #24
Dick
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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.
 
  • #25
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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
 

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