M1 position vectors (June 2013 question 8)

Hi guys, I'm really stuck on this question.

I solved a) by writing an equation for the displacement of the helicopter defined by t, added to the original postion vector at the light house.

For b), I know I have to create two equations using the components of the expression above and solve for a value of t, I just don't understand why am I equating the position vector of the helicopter above to that of the rock? Surely the helicopter is in the air & it's height never changes. Hence it can only have the same x component as the rock's position vector? :/

(edited 7 years ago)

Reply 1

TheBBQ

21

y component does not correlate to height.

The best way to think of it is to imagine a compass. Say North is y and East is x, thus South correlates to -y and West is -x.

So if the helicopter is directly above the rock, it will share the same coordinates. (x, y) Essentially x = i, y = j

If you walked towards the rock and stood on it, you would be standing on the same coordinates as the helicopter. You're concerned about the position from the origin, not the vertical height from the ground. You're given that the helicopter is at a constant height above sea level so you're not concerned about it.

Don't turn a 2D problem into a 3D problem :tongue:

(edited 7 years ago)

Reply 2

Serine

OP

1

Original post by TheBBQ

y component does not correlate to height.

The best way to think of it is to imagine a compass. Say North is y and East is x, thus South correlates to -y and West is -x.

So if the helicopter is directly above the rock, it will share the same coordinates. (x, y) Essentially x = i, y = j

If you walked towards the rock and stood on it, you would be standing on the same coordinates as the helicopter. You're concerned about the position from the origin, not the vertical height from the ground. You're given that the helicopter is at a constant height above sea level so you're not concerned about it.

Don't turn a 2D problem into a 3D problem :tongue:

Thank you!
Lol that's exactly what my teacher said to me today, I just didn't understand what she meant by it.

Is it better to think of a position vector a bit like a coordinate on a map - where exactly on the land the helicopter and a rock is irrelevant, but they are at same relative displacement northwards and eastwards (or south and west) from 0,0? Because this is what I'm have trouble understanding!! :smile:

Reply 3

TheBBQ

21

Original post by Serine

Thank you!
Lol that's exactly what my teacher said to me today, I just didn't understand what she meant by it.

Is it better to think of a position vector a bit like a coordinate on a map - where exactly on the land the helicopter and a rock is irrelevant, but they are at same relative displacement northwards and eastwards (or south and west) from 0,0? Because this is what I'm have trouble understanding!! :smile:

You're welcome :smile:

Vectors can be a bit tricky at first but when you understand them, the questions become very simple.

Yes, exactly that. I could choose a completely different point to be the origin and thus the position vector would be different, the positions of the helicopter and rock would be the same relative to each other.

Imagine that I told you about a house 50m west from me, but you were 50m north of me. It doesn't change where exactly it is, but we would both require different directions to get there. I would have to walk west, but you would have to walk southwest, thus it would have a different position vector from each of our perspectives if we chose our starting points as the origin. But to a neighbour of that house, it would obviously not have a different position for him regardless of wherever we chose our origins.

It's all about relative distances, not absolutes.

(edited 7 years ago)

M1 position vectors (June 2013 question 8)

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