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M1 Vectors

At 2pm the coastguard spots a rowing dinghy 500m due South of his observation point. The dinghy has constant velocity(2i\mathbf{i}+3jms−1\mathbf{j}ms^{-1}

a)Find in terms of t, the position vector of the dinghy t seconds after 2pm
I got 2ti\mathbf{i}+(-500+3t)i\mathbf{i}


b)Find the distance of the dinghy from the observation point at 2:05pm

Help pls on part b no idea what to do talk me through what to do.

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Original post by thefatone
At 2pm the coastguard spots a rowing dinghy 500m due South of his observation point. The dinghy has constant velocity(2i\mathbf{i}+3jms−1\mathbf{j}ms^{-1}

a)Find in terms of t, the position vector of the dinghy t seconds after 2pm
I got 2ti\mathbf{i}+(-500+3t)i\mathbf{i}


b)Find the distance of the dinghy from the observation point at 2:05pm

Help pls on part b no idea what to do talk me through what to do.


Draw a diagram and see if it becomes clearer then :borat:
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thefatone
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Original post by SeanFM
Draw a diagram and see if it becomes clearer then :borat:


this has done

absolutely nothing for me i'm not seeing anything
Original post by thefatone
this has done

absolutely nothing for me i'm not seeing anything


What does your diagram look like?

Can you see any way of finding the distance between where the dinghy is and the observation point?
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Original post by SeanFM
What does your diagram look like?

Can you see any way of finding the distance between where the dinghy is and the observation point?


Original post by thefatone


What lovely paper :tongue:

You have fallen into a trap - look carefully at the units in the question and then the time it asks you where the dingy is in the question.

But with that diagram you can still work out the method of finding the distance between the position and the origin.

How do you find the distance between the origin and the position? (You can think of them as x and y co-ordinates if you like).

Hint:

Spoiler

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thefatone
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Original post by SeanFM
What lovely paper :tongue:

You have fallen into a trap - look carefully at the units in the question and then the time it asks you where the dingy is in the question.

But with that diagram you can still work out the method of finding the distance between the position and the origin.

How do you find the distance between the origin and the position? (You can think of them as x and y co-ordinates if you like).

Hint:

Spoiler



no idea, 100% clueless
Original post by thefatone
no idea, 100% clueless


Okay, let's look at an example. If you had the point (3,4) on a graph and I asked you to find the distance between that and the origin, how would you do it?

Hint:

Spoiler

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Original post by SeanFM
Okay, let's look at an example. If you had the point (3,4) on a graph and I asked you to find the distance between that and the origin, how would you do it?

Hint:

Spoiler



pythagoras
Original post by thefatone
pythagoras


Correct :borat: so, how does that help with anything?
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Original post by SeanFM
Correct :borat: so, how does that help with anything?


it doesn't
Original post by thefatone
it doesn't


There is not much more I can say without giving away the answer :tongue: so I'll go over what I've said before:

1. Remember to look at the units in the question and correct your position vector at 2:05.

2. Try and find the distance between the position vector and the origin using ...
Reply 12
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thefatone
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Original post by SeanFM
There is not much more I can say without giving away the answer :tongue: so I'll go over what I've said before:

1. Remember to look at the units in the question and correct your position vector at 2:05.

2. Try and find the distance between the position vector and the origin using ...


where's the 90° angle?
Reply 13
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thefatone
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Original post by SeanFM
There is not much more I can say without giving away the answer :tongue: so I'll go over what I've said before:

1. Remember to look at the units in the question and correct your position vector at 2:05.

2. Try and find the distance between the position vector and the origin using ...


i don't understand the time aspect of things, do i count time in hours or seconds?
Original post by thefatone
where's the 90° angle?


Well, where is the 90 degree angle between (0,0) and (3,4)?

For your time question, look at the question and see if you can work it out.

(I am deliberately giving you as little as possible so you can work it out for yourself :h:)
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Original post by SeanFM
Well, where is the 90 degree angle between (0,0) and (3,4)?

For your time question, look at the question and see if you can work it out.

(I am deliberately giving you as little as possible so you can work it out for yourself :h:)


between the x-axis and line parallel to the y-axis but i'm not seeing how this helps me do this question :/ i don't know if it's a right angled triangle.

no idea, it's literally a guess i have no idea what i count time as maybe 5? 0.5? 0.005? i really don't know
Original post by thefatone
between the x-axis and line parallel to the y-axis but i'm not seeing how this helps me do this question :/ i don't know if it's a right angled triangle.

no idea, it's literally a guess i have no idea what i count time as maybe 5? 0.5? 0.005? i really don't know


(3,4) means that from (0,0) you go 3 to the right and 4 up. So you can draw a line 3 units to the right then 4 units up from that point, and then a straight line from (0,0) to (3,4) and there is your right angled triangle. The straight line represents the distance between the two points.

I'll give you another hint for the time - 2:05 is 5 minutes after 2 o'clock, and your velocity vector is measured in metres per second.
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Original post by SeanFM
(3,4) means that from (0,0) you go 3 to the right and 4 up. So you can draw a line 3 units to the right then 4 units up from that point, and then a straight line from (0,0) to (3,4) and there is your right angled triangle. The straight line represents the distance between the two points.

I'll give you another hint for the time - 2:05 is 5 minutes after 2 o'clock, and your velocity vector is measured in metres per second.


i see so the time t is 300 then? so i sub in 300 as t? .-.



sooooo

i get
600i\mathbf{i}+400j\mathbf{j}?
(edited 7 years ago)
Original post by thefatone
i see so the time t is 300 then? so i sub in 300 as t? .-.



sooooo

i get
600i\mathbf{i}+400j\mathbf{j}?


Correct. :borat: (as long you understand why, if you don't just say :tongue: :h:)

Okay, you're almost there. What next?
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Original post by SeanFM
Correct. :borat: (as long you understand why, if you don't just say :tongue: :h:)

Okay, you're almost there. What next?


good point what next? i have no idea we have distance... final distance, time, constant velocity so this means a=0

soooo i'm done? 600i\mathbf{i}+400j\mathbf{j} is my final answer? no... pythagoras

so 6002+4002=721m\sqrt{600^2 +400^2} = 721 m thanks a ton :smile:

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