Expression for derivative of distance from point away from arc

MontanaSosa

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See picture. The question is, given some point P in front of the circular arc segment, what is dL/dt? where dt is the length traveled along the arc, and L is the distance from the point to the arc at t.
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See picture. The question is, given some point P in front of the circular arc segment, what is dL/dt? where dt is the length traveled along the arc, and L is the distance from the point to the arc at t.
View attachment 10793
We need to have more information.

Please post the exact question presented to you.
 
The problem wasn't given to me, I was just wondering how this could be done. The expression can be general, the radius of curvature, the location of the point, etc. Variables can be defined as needed.
 
The problem wasn't given to me, I was just wondering how this could be done. The expression can be general, the radius of curvature, the location of the point, etc. Variables can be defined as needed.
This is a problem that has been solved in Mechanics (more specifically college level Dynamics), using plane geometry, trigonometry and calculus. Start reading a book in Dynamics - the topic specific to this would be the "Kinematics of particle in plane motion".

If you have more specific question - let us know.
 
I looked at some dynamics references but couldn't find anything relating specifically to how the length to a point varies. I understand the radius of curvature is different at every point. If we write the path as a general function f(x), I have that dt = sqrt(dx^2 + df^2), but I am not sure about dL? Any hints would be much appreciated.
 
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