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Calculus Based Dynamics Problem

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An object travels with a constant speed "v" in the x-y plane over a feature that is described by the equation {see attachment}.
Given that the instantaneous radius of curvature for any plane curve is: {see attachment}, find the minimum value of "v" that makes the object "weightless" at the apex.
Take "g" to equal 9.81 m/s[squared]
Neglect object size.

*Please see attachment for functions and diagram.

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The solution finds the minimum value of "v" that makes the object "weightless" at the apex.

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