# I need help with this question about vectors

## 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)

PeroK
Homework Helper
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2020 Award
Have you drawn a diagram?

FactChecker and berkeman
LCKurtz
Homework Helper
Gold Member

## 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
phinds
Gold Member
Have you drawn a diagram?
Yeah. What he said.

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

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

phinds
Gold Member
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.

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?

phinds
Gold Member
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?

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

phinds
Gold Member
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.

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

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

@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

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

LCKurtz
Homework Helper
Gold Member
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?

phinds
Gold Member
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)

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

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

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LCKurtz
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.

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

LCKurtz
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.

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

Mark44
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?

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