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Edexcel M1 - Vectors

I'm having problems with this question :frown:

A small boat S, drifting in the sea, is modelled as a particle moving in a straight line at constant speed. When first sighted at 0900, S is at a point with position vector (-2i-4j)km relative to a fixed origin O, where i and j are unit vectors due east and due north respectively. At 0940, S is at the point with position vector (4i-6j)km. At time t hours after 0900, S is at the point with position vector skm.

a) Calculate the bearing on which S is drifting.
b) Find an expression for s in terms of t.
at 1100 a motor boat M leaves O and travels with constant velocity (pi + qj)kmh-1
c) Given that M intercepts S at 1130, calculate the value of p and the value of q

I managed to find a) which is 108degrees. For the b) part, don't I need the velocity of S to apply the formula of r=r0+vt? :confused:

Also, to find c) I need to get the equation at b) first right?
Reply 1
Original post by Akiraryuu
I'm having problems with this question :frown:

A small boat S, drifting in the sea, is modelled as a particle moving in a straight line at constant speed. When first sighted at 0900, S is at a point with position vector (-2i-4j)km relative to a fixed origin O, where i and j are unit vectors due east and due north respectively. At 0940, S is at the point with position vector (4i-6j)km. At time t hours after 0900, S is at the point with position vector skm.

a) Calculate the bearing on which S is drifting.
b) Find an expression for s in terms of t.
at 1100 a motor boat M leaves O and travels with constant velocity (pi + qj)kmh-1
c) Given that M intercepts S at 1130, calculate the value of p and the value of q

I managed to find a) which is 108degrees. For the b) part, don't I need the velocity of S to apply the formula of r=r0+vt? :confused:

Also, to find c) I need to get the equation at b) first right?


For part (b) you need to use r=r0+vt, and you need to sub in the velocity which you found in part (a).
Reply 2
Original post by raheem94
For part (b) you need to use r=r0+vt, and you need to sub in the velocity which you found in part (a).

Isn't part a) asking for the bearing? I don't see any velocity equation there :confused:
Reply 3
Original post by Akiraryuu
Isn't part a) asking for the bearing? I don't see any velocity equation there :confused:


Yes, part (a) is asking for the bearing. There will be alternative techniques to do part (a) but the way i did that required to find the velocity vector.

Just find the velocity vector and do part (b).
Reply 4
Original post by raheem94
Yes, part (a) is asking for the bearing. There will be alternative techniques to do part (a) but the way i did that required to find the velocity vector.

Just find the velocity vector and do part (b).

Oh! I solved part a) using trig. That's the problem, I have no idea how to get the velocity vector from the two position vector equations.
Reply 5
Original post by Akiraryuu
Oh! I solved part a) using trig. That's the problem, I have no idea how to get the velocity vector from the two position vector equations.


You know the formula, r=r0+vt \displaystyle r=r_0+vt

We know that r0=2i4j \displaystyle r_0 = -2i-4j

We know that at 0940(which is t=2/3 if we measure time in hours) r=4i6j \displaystyle r=4i-6j

So using the formula, r=r0+vt \displaystyle r=r_0+vt , we get, 4i6j=2i4j+23v \displaystyle 4i-6j =-2i-4j+\frac23v
Reply 6
Original post by raheem94
You know the formula, r=r0+vt \displaystyle r=r_0+vt

We know that r0=2i4j \displaystyle r_0 = -2i-4j

We know that at 0940(which is t=2/3 if we measure time in hours) r=4i6j \displaystyle r=4i-6j

So using the formula, r=r0+vt \displaystyle r=r_0+vt , we get, 4i6j=2i4j+23v \displaystyle 4i-6j =-2i-4j+\frac23v

Oh god, why didn't I see the connection sooner? Gah. Thank you so so so much.
Reply 7
Original post by Akiraryuu
Oh god, why didn't I see the connection sooner? Gah. Thank you so so so much.


No problem.

Do you know how to do part (c)?
Reply 8
Original post by raheem94
No problem.

Do you know how to do part (c)?

Yep, got it. My only problem was finding the vector equation. Thanks again. :smile:
Reply 9
how do we find the time ?
Reply 10
A boat B is moving with constant velocity. At noon, B is at the point with position vector
(3i 4j) km with respect to a fixed origin O. At 1430 on the same day, B is at the point
with position vector (8i + 11j) km.
(a) Find the velocity of B, giving your answer in the form pi + qj.

how to find the time :bricks: im stuck in this
Original post by sowmyaraju
A boat B is moving with constant velocity. At noon, B is at the point with position vector
(3i 4j) km with respect to a fixed origin O. At 1430 on the same day, B is at the point
with position vector (8i + 11j) km.
(a) Find the velocity of B, giving your answer in the form pi + qj.

how to find the time :bricks: im stuck in this


i think you need to use r=Ro+vt
so (8i+11j)=(3i-4j) + 2.5v
(8i+11j) - (3i - 4j) =2.5v
(5i + 15j) = 2.5v
v= 2i + 6j
is that the right answere?
What does it mean when something says find the time when X is moving 'due east of something'

equate the i components?
Reply 13
Original post by Obscenedilemma
What does it mean when something says find the time when X is moving 'due east of something'

equate the i components?


If X moves due east of Y then the j components of both are same, so equate the j components.
hey......can sm1 hlp me wid dis question
given that a=2i+5j and b=3i-j find X if a+Xb is parallel to vector i
Original post by backstreet1
hey......can sm1 hlp me wid dis question


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