# Circles, Centre, parabolas, motionWatch

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#1
Come up to a bit of a strange question here and I’m stuck. The first section seems focused on the ‘Directrix of a Parabola’. However the part I’m stuck on it doesn’t seem necessary to use/understand that anyway.

Question here:

I started of with this following the hint

But I’m not sure what to do next? Assuming I’ve got that correct then I’m not sure what I could do to make theta independent of the distance (radius) unless v or t was equal to zero…

Would really appreciate help with this one!

More (higher resolution?) pictures of the question and the other parts here: https://m.imgur.com/a/4VTHSvw
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1 week ago
#2
Sorry I can't help (far too rusty and haven't done this sort of stuff since circa 1982!). But what a beautiful bit of maths!
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1 week ago
#3
(Original post by Maximus 190)
Come up to a bit of a strange question here and I’m stuck. The first section seems focused on the ‘Directrix of a Parabola’. However the part I’m stuck on it doesn’t seem necessary to use/understand that anyway.

Question here:

I started of with this following the hint

But I’m not sure what to do next? Assuming I’ve got that correct then I’m not sure what I could do to make theta independent of the distance (radius) unless v or t was equal to zero…

Would really appreciate help with this one!

More (higher resolution?) pictures of the question and the other parts here: https://m.imgur.com/a/4VTHSvw
Although he's deleted it, mqb2766 was on the right lines.

If you consider a particle going straight up and one going straight down, IF they lie on a circle, those two particle's positions must form the extermities of a diameter and their midpoint must be the centre of the circle. Hence, if it is a circle, the centre of circle must be ....

Then continue with your Pythagoras, and theta will be eliminated.... showing it is a circle (dependent on t).
Last edited by ghostwalker; 1 week ago
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1 week ago
#4
(Original post by ghostwalker)
Although he's deleted it, mqb2766 was on the right lines.

If you consider a particle going straight up and one going straight down, IF they lie on a circle, those two particle's positions must form the extermities of a diameter and their midpoint must be the centre of the circle. Hence, if it is a circle, the centre of circle must be ....

Then continue with your Pythagoras, and theta will be eliminated.... showing it is a circle (dependent on t).
Yeah, thought it was ~1/2 right but was trying to sort out the 1/2 wrong bit :-)
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#5
(Original post by ghostwalker)
Although he's deleted it, mqb2766 was on the right lines.

If you consider a particle going straight up and one going straight down, IF they lie on a circle, those two particle's positions must form the extermities of a diameter and their midpoint must be the centre of the circle. Hence, if it is a circle, the centre of circle must be ....

Then continue with your Pythagoras, and theta will be eliminated.... showing it is a circle (dependent on t).
Okay I have found the centre and radius by assuming it is a circle and using the fact that the particles going up and down are opposite ends, midpoint is centre etc. This gives me the radius as a function of time = vt which is correct. However, when proving it is a circle independent of theta I don’t see what you mean my continue with my Pythagoras. Seems like a huge mess.
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6 days ago
#6
(Original post by Maximus 190)
Okay I have found the centre and radius by assuming it is a circle and using the fact that the particles going up and down are opposite ends, midpoint is centre etc. This gives me the radius as a function of time = vt which is correct. However, when proving it is a circle independent of theta I don’t see what you mean my continue with my Pythagoras. Seems like a huge mess.

You've worked out where the centre must be. So, why didn't you just replace c in your original Pythagoras. Everything simplifies and theta vanishes.
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#7
(Original post by ghostwalker)
You've worked out where the centre must be. So, why didn't you just replace c in your original Pythagoras. Everything simplifies and theta vanishes.
Oh yeah, very cool! Thanks
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