Water slide

A water slide allows young children to slide down a chute at rapid speeds in complicated shapes. Slides have two shapes associated with them, the shape of a cross section of the slide and the shape the slide makes as it curves around. You own an amusement park with a giant water slide. The slide cross section has the shape of a parabola with height \(y=x^2/2\). The slide itself in one part curves around as a segment of a horizontal circle of radius \(5~\mbox{m}\). If the maximum height of the cross section of the slide is \(1~\mbox{m}\), what is the maximum speed with which kids can slide through the curved part of the slide without falling out?

Details and assumptions

  • The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).
  • Treat the kids as point masses.
  • Assume the speed of the kid is a constant throughout this section.
  • Neglect friction.

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