The Brachistochrone Problem: Show that if the particle is projected withan initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloidpassing through the two points with a cusp at a height z above the initialpoint given by v02 = 2gz.

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The Brachistochrone Problem: Show that if the particle is projected with
an initial kinetic energy 1/2 m v₀²that the brachistochrone is still a cycloid
passing through the two points with a cusp at a height z above the initial
point given by v₀² = 2gz.

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The Brachistochrone Problem: Show that if the particle is projected with an initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloid passing through the two points with a cusp at a height z above the initial point given by v02 = 2gz