# I with this question about vectors

lioric

## Homework Statement

At noon two boats P and Q have a position vector (i+7j)km and (3i+8j)km respectively to the origin O.
i and j are unit vectors in direction to East and north respectively
P is moving south east at 5√2 km/h and Q is moving at a constant velocity of (6i+5j) km/h
At time t after noon the position vectors of P and Q with respect to O are p km and Q km
a) show that the velocity of P is ( 5i + 5j)
b) find the time to the nearest minute when Q is north east of P

## Homework Equations

Phythogorus theorum a^2 = b^2 + c^2

## The Attempt at a Solution

I have done part a)
Where if the velocity is (5i+5j), then if you use phythogorus theorum where √(5^2+5^2) I get 5√2

I don't know how to do part b)

## Answers and Replies

Homework Helper
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Have you drawn a diagram?

• FactChecker and berkeman
Homework Helper
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## Homework Statement

At noon two boats P and Q have a position vector (i+7j)km and (3i+8j)km respectively to the origin O.
i and j are unit vectors in direction to East and north respectively
P is moving south east at 5√2 km/h and Q is moving at a constant velocity of (6i+5j) km/h
At time t after noon the position vectors of P and Q with respect to O are p km and Q km
a) show that the velocity of P is ( 5i + 5j)
The red quotes seem inconsistent.

• FactChecker
Gold Member
2021 Award
Have you drawn a diagram?
Yeah. What he said.

@lioric discussing this kind of problem without a vector diagram is a waste of time.

lioric
Yeah. What he said.

@lioric discussing this kind of problem without a vector diagram is a waste of time.
Yes I have drawn a diagram

Gold Member
2021 Award
Yes I have drawn a diagram
Uh ... and do you plan to share it with US? You ARE asking us to discuss it after all.

lioric
But my main problem is figuring out the wording of the question
Is the question asking me to find the time when Q is at a bearing of 45 degrees of P?

Gold Member
2021 Award
But my main problem is figuring out the wording of the question
Is the question asking me to find the time when Q is at a bearing of 45 degrees of P?
What does "North East" mean?

lioric
What does "North East" mean?
East is 90 degrees from North
North east is the bisection of that
It's the line equidistant from the East and the north
The angle is 45 degrees from north

Gold Member
2021 Award
East is 90 degrees from North
North east is the bisection of that
It's the line equidistant from the East and the north
The angle is 45 degrees from north
There are two lines that are 45 degrees from North. Yes, I DO know what you mean but my point is that without a vector diagram, again, this discussion is useless.

Homework Helper
Gold Member
@lioric: Are you ever going to respond to post #3 with a correct statement of the problem?

Gold Member
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@lioric: Are you ever going to respond to post #3 with a correct statement of the problem?
AND a vector diagram !

lioric
@lioric: Are you ever going to respond to post #3 with a correct statement of the problem?
What can I say about what the red quotes say? It's what the question said. Word to word

lioric
AND a vector diagram !
I have drawn the diagram
And I can solve the problem when I'm sure about the north east part
I just need to know the exact meaning of that
Just clearing my doubts

Homework Helper
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What can I say about what the red quotes say? It's what the question said. Word to word
Do you understand that the direction and vector I quoted in red do not agree?

Gold Member
2021 Award
Do you understand that the direction and vector I quoted in red do not agree?
He might have figured that out if he had done a correct vector diagram, which is one reason I keep telling him to do one (AND show it to us so we can help)

lioric
Sorry that's a typo
It's 5i-5j
Sorry

lioric
At noon two boats P and Q have a position vector (i+7j)km and (3i-8j)km respectively to the origin O.
i and j are unit vectors in direction to East and north respectively
P is moving south east at 5√2 km/h and Q is moving at a constant velocity of (6i+5j) km/h
At time t after noon the position vectors of P and Q with respect to O are p km and Q km
a) show that the velocity of P is ( 5i - 5j)
b) find the time to the nearest minute when Q is north east of P

This is the correct one

lioric #### Attachments

Homework Helper
Gold Member
Sorry that's a typo
It's 5i-5j
Sorry
That and the now changed original position of Q. So now you can show us how you calculate Q and P's positions at time t. Then think about what must be true about Q-P for Q to be northeast of P.

lioric
That and the now changed original position of Q. So now you can show us how you calculate Q and P's positions at time t. Then think about what must be true about Q-P for Q to be northeast of P.
Q must be at a 45 degrees bearing to P

Homework Helper
Gold Member
I posted: "So now you can show us how you calculate Q and P's positions at time t". Which you ignored.

lioric
I posted: "So now you can show us how you calculate Q and P's positions at time t". Which you ignored.
We use r=r0 + vt

Mentor
We use r=r0 + vt
LCKurtz's question was more specific than this. In other words, what were your calculations for Q and P at an arbitrary time t?

lioric
LCKurtz's question was more specific than this. In other words, what were your calculations for Q and P at an arbitrary time t?
Let's say at time t the position of P is p and the position of Q is q so in terms of p and q and t I can give the new position of P as
r=r0+vt
= (i+7j) + (5i-5j)t
=i+7j + 5it-5jt
=(1+5t)i + (7+5t)j

And new position for Q as
r=r0+vt
=(3i-8j) + (6i+5j)t
=3i-8j + 6it+5jt
=(3+6t)i + (5t-8)j

Homework Helper
Gold Member
Is there some reason you don't simplify those? Anyway, now you have them, what next? There was more in post #20. Tell us what you are thinking or why you are stuck.

lioric
Is there some reason you don't simplify those? Anyway, now you have them, what next? There was more in post #20. Tell us what you are thinking or why you are stuck.
Well you can see how I have drawn the vector diagram I drew it true to the i j to x y vector coordinates. I just don't know how to go about the question. Some hints would be helpful

Homework Helper
Gold Member
You have had some hints. In post #20 I asked you about Q - P. Have you even calculated that yet? Are you going to show us what you get? Have you thought about whether it points Northeast? Or how you would tell? Neither I nor anyone else on this board is going to work it for you.

You don't need any diagrams. The key is to subtract the vector velocity and position of P from Q. This makes P the new origin and gives you a new location and new vector velocity for Q. You can now use those velocity components to figure out when the two position components will be equal which is when the position of Q is north-east of P.

lioric
You don't need any diagrams. The key is to subtract the vector velocity and position of P from Q. This makes P the new origin and gives you a new location and new vector velocity for Q. You can now use those
velocity components to figure out when the two position components will be equal which is when the position of Q is north-east of P.
Thank you all for your help
So the position of
P = (i+7j) with v= (5i-5j)
Q=(3i-8j) with v=(6i+5j)
Already Q is on the east side of P and the rate at with Q moves in x axis is faster than P
So therefore Q will always be on the east side of P
When we look at the y axis it seems that P is moving down at the same rate as Q is moving up
So the moment these two meet in y plan would be the time that Q is exactly on the east of P
So using speed = distance /time
Distance= 7-(-8)= 15
To find mid position 15/2 =7.5
Speed = 5
Time=distance/speed
=7.5/5=1.5hrs
At this time the two ships will be is line in the
With a gap in the x axis
Anything more than 1.5 hours and Q will be in the NE section of P

How's this?
Ok?

Homework Helper
Gold Member
How's that? Not good. You haven't even used ##t##.

If you had actually read and responded to my posts you would have had this problem solved a week ago. You haven't simplified your answer in post #25 or responded to post #28. Until you do you will hear nothing more from me.

lioric
How's that? Not good. You haven't even used ##t##.

If you had actually read and responded to my posts you would have had this problem solved a week ago. You haven't simplified your answer in post #25 or responded to post #28. Until you do you will hear nothing more from me.
I'm sorry about that
Was away for some time and no internet there
But I'll start working on this now.
Ok so simplifying the new position of P
(1+5t)i + (7+5t)j
P= i+5ti + 7j+5tj
New position of Q
(3+6t)i + (5t-8)j
Q= 3i+6ti + 5tj-8j

Q-P
(3i-8j)-(i+7j)
=(2i-15j)

Homework Helper
Gold Member
Make sure you are using the correct numbers as given in post #18.
When you "simplify" a vector it should look like (...)i + (...)j, one i term and one j term.
Your final answer for Q-P at time t must have a "t" in it.
Then we can talk about whether it points NE.

lioric
Post 18

At noon two boats P and Q have a position vector (i+7j)km and (3i-8j)km respectively to the origin O. i and j are unit vectors in direction to East and north respectively P is moving south east at 5√2 km/h and Q is moving at a constant velocity of (6i+5j) km/h

lioric
Make sure you are using the correct numbers as given in post #18.
When you "simplify" a vector it should look like (...)i + (...)j, one i term and one j term.
Your final answer for Q-P at time t must have a "t" in it.
Then we can talk about whether it points NE.
I m very confused
In post #25 it seems that the vectors are in the format that you asked (....)i+(...)j and you asked me to simply them. So I expanded them and now your asking me to revert them back again.