Kinematics

[Shreyash]

Point A moves uniformly with velocity v so that vector v is continually aimed at point B, which in its turns moves rectilinearly and uniformly with velocity u

[Tuvok]

....and?

[gingejbee]

...and speed (or is that velocity?) kills!

[factor-fiction]

You can add the rest of the question by replying to your original question.

[bert_h]

The point then describes a curve called the "tractrix".

For a competent mathematical explanation, see http://mathworld.wolfram.com/Tractrix.html.

Wikipedia and similar sites may have an explanation in simpler language.

[Peter Pedant]

yeah its true ( as a question Bert ) that if you twizzle the tractrix around the asymptote
you get a pseudosphere

which is inn fact the Einstein relativity space in which we live innit ?

[bert_h]

Well, PP, I'd forgotten the term 'pseudosphere', but the solid generated by rotating the tractrix does indeed have uniform negative curvature all over its surface, which has something to do with Lobachevsky. Happy googling!

[factor-fiction]

The full question is:

Point A moves uniformly with velocity v so that the vector is continually aimed at point B which in its turn moves rectilinearly and uniformly with velocity u

[factor-fiction]

Sorry- half my answer didn't appear then.
I'll try again

[factor-fiction]

Sheyrash's initial question and my attempt to finish it off both failed because typing a 'less than' sign in AnswerBank terminates the post. I will try again and will use LT to represent the 'less than' sign.

Here is the full question.

Point A moves uniformly with velocity v so that the vector is continually aimed at point B which in its turn moves rectilinearly and uniformly with velocity u LT v. At the initial moment of time v is perpendicular to u and the points are separated by a distance L. How soon will the point converge?

I can provide the answer but would be interested to see how far you have got first

[vascop]

I'm a bit confused. Are you saying that initially v is perpendicular to u? So point A is initially NOT moving towards B, is that right? And there are no accelerations (forces)?

[factor-fiction]

Yes, initially the vector V is perpendicular to the vector U. Point A and B move at a uniform rate with Point B moving rectilinearly.

If it helps, the solution given is that they meet after time T= LV/(V²-U²)

[vascop]

Still don't get it. You say that the velocity of point A always points towards B, but not initially?

[factor-fiction]

I'm just repeating the question. I think the question should have said "aimed at" in inverted commas

[vascop]

Maybe I'm missing something, but I don't understand the problem as stated and so i can't have a go at solving it. Can you state the problem in your own words ff, and then I might get it. Thanks

[vascop]

Is V the velocity in general and v the initial value of V?

[factor-fiction]

The problem comes from General Problems in Physics by IE Irodo.

There is a reference to it here: http://physics.stackexchange.com/questions/121569/finding-the-time-of-convergence-for-this-system-of-particles

and here: http://www.wopho.org/problempedia-problem-detail.php?type=1&;pid=1&id=27

and a full solution with diagram is here:
http://irodovphysicssolutionrks.blogspot.co.uk/2012/06/113.html

[vascop]

Thanks FF, I'll take a look.

[vascop]

Factor
I've looked at the solution you gave a link to and I must say it's very poorly explained. After looking at it for about an hour I have finally understood it. Do you understand it yourself? The subtle bit is understanding what x stands for in dx/dt. If you don't then you won't understand the solution. The reason it's confusing is because he has labelled his horizontal axis x but the x in dx/dt is not referring to the x coordinate of A or B. What is it referring to? Can you tell me? I challenge you! :)
Very difficult for A-level students - too difficult in my view without a hint to point them in the right direction. I'll submit my solution if you want me to and you can tell me if you agree.

[factor-fiction]

I'll have a look tomorrow but I no longer have the patience for this sort of stuff. I lapped it up as a maths student 35-40 years ago but since then have never gone beyond teaching GCSE/first year A level Maths and now can't be bothered with anything more demanding

[Baldric]

http://www.wopho.org/problempedia-problem-detail.php?type=1&;pid=1&id=27