The Incredible Shrinking Majority....
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Kinematics
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
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The point then describes a curve called the "tractrix".
For a competent mathematical explanation, see http://
Wikipedia and similar sites may have an explanation in simpler language.
For a competent mathematical explanation, see http://
Wikipedia and similar sites may have an explanation in simpler language.
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
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
The problem comes from General Problems in Physics by IE Irodo.
There is a reference to it here: http://
and here: http://
and a full solution with diagram is here:
http://
There is a reference to it here: http://
and here: http://
and a full solution with diagram is here:
http://
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.
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.
