
#19
Jan713, 06:28 AM

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P: 16,466





#20
Jan713, 06:30 AM

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P: 40,872

(If you really believe that the speeding car does not have the slightest movement relative to you, why not reach out and touch it?) 



#21
Jan713, 07:00 AM

P: 14

I am thinking about it. 



#22
Jan713, 07:03 AM

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P: 16,466





#23
Jan713, 07:10 AM

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P: 16,466

Just for reference, if an object is moving in a straight line at speed v wrt me and its closest point of approach is a distance r_{0} from me then the distance from me is [itex]r(t)=\sqrt{v^2 t^2 + {r_0}^2}[/itex] where t is the time before or after the point of closest approach.
[tex]r'(t)=\frac{v^2 t}{\sqrt{v^2 t^2 + {r_0}^2}}[/tex] [tex]r''(t)=\frac{v^2 {r_0}^2}{\left(v^2 t^2 + {r_0}^2\right)^{3/2}}[/tex] Again, r' is the time rate of change of the distance between the object and me, it is not the speed of the object wrt me. That is v. 



#24
Jan713, 11:46 AM

P: 14





#25
Jan813, 01:39 AM

P: 500

The OP's question is a good one and clearly shows an intuitive reach that exceeds his grasp of some basics... just needs clarification of fundamentals about lengths and times  values, deltas, infinitesimal differentials, and instantaneous values.




#26
Jan813, 05:37 AM

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P: 21,994

A reference frame is a set of xy (and maybe z) coordinates. Speed is the change in position in that coordinate system (divided by time). If you happen to be located at the origin of that coordinate system, the object you are observing does not have to be moving directly toward or away from you to have a measurable speed. Consider, for example, constant speed motion from (3,0) to (0,3) in a coordinate system. Examples of 1 dimensional motion are often used to simplify problems, but that shouldn't trick one into thinking motion is all directly toward or away from the origin of the reference frame. In the Navy, we used what is called a "maneuvering board" to transform bearing and distance to a target (polar coordinates) to two different Cartesian coordinate systems centered on our ship, to calculate the distance and speed of another ship relative to us (and closest point of approach), in our moving frame of reference and in a frame stationary with respect to the water: http://gcaptain.com/maritime/tools/files/MoBoard.pdf 


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