A highway has an exit ramp that begins at the origin of the coordinate system an

Question

A highway has an exit ramp that begins at the origin of the coordinate system and follows the curve given by y =1/32 X^(5/2) to the point (4,1)(see figure) Then it follows a circular path whose curvature is given by the curve at (4,1) What is the circular arc? Explain why the curve and the circular arc should have the same curvature at (4,1). http://books.google.com/books?id=hcugW8A7cB8C&pg;=PA884&lpg;=PA884&dq;=a+highway+has+an+exit+ramp+that+begins+at+the+origin+of+a+coordinate+system+and+follows+the+curve&source;=bl&ots;=ensq9uQwZF&sig;=6So-ihTyE-68VCRp2L2X1vi5a7o&hl;=en&sa;=X&ei;=TrDPUJzUJuXl0QHjm4Bw&ved;=0CFAQ6AEwBQ#v=onepage&q;=a highway has an exit ramp that begins at the origin of a coordinate system and follows the curve&f;=false

Explanation / Answer

Please read these articles, these will explain your answer. These are handy

1.http://www.kaj.pr.radom.pl/prace/Biarcs.pdf

2. http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&cad=rja&ved=0CG8QFjAI&url=http%3A%2F%2Fcourses.washington.edu%2Fcive316%2Flectures%2Fpps_lectures%2FHorizontal_Curves.pps&ei=CxLQUMy9C_SZ0QXV0oCABA&usg=AFQjCNGlc2wLmpNPShI73Bcu5HvWCSYV3A&sig2=6DvlrCP9qD-7lYFXdXmlIg&bvm=bv.1355534169,d.Yms

3. http://www.math.technion.ac.il/S/rl/docs/parabola.pdf

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