[Akiraryuu]

I'm having problems with this question

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?

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

[raheem94]

(Original post by Akiraryuu)
I'm having problems with this question

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?

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).

[Akiraryuu]

(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

[raheem94]

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

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).

[Akiraryuu]

(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.

[raheem94]

(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,

We know that

We know that at 0940(which is t=2/3 if we measure time in hours)

So using the formula, , we get,

[Akiraryuu]

(Original post by raheem94)
You know the formula,

We know that

We know that at 0940(which is t=2/3 if we measure time in hours)

So using the formula, , we get,

Oh god, why didn't I see the connection sooner? Gah. Thank you so so so much.

[raheem94]

(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)?

[Akiraryuu]

(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.

[sowmyaraju]

how do we find the time ?

[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 im stuck in this

[sheepzibaa]

(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 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?

[Obscenedilemma]

What does it mean when something says find the time when X is moving 'due east of something'

equate the i components?

[raheem94]

(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.

[backstreet1]

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

[TenOfThem]

(Original post by backstreet1)
hey......can sm1 hlp me wid dis question

You need to start a thread not add to an old one