The One With Slides

Calculus Level 1

A slide in the shape of a cycloid cusp is set up at a carnival, as shown. Among Chandler, Rachel, Ross, and Phoebe, who will take the least time to reach the bottom of the slide?

Details and Assumptions:

  • Chandler, Phoebe, Rachel, and Ross are \(25,\,20,\,15,\) and \(5\) meters away, respectively, from the center of the slide.
  • Initially, everyone is at rest and they take turns sliding down the slope.
  • Gravity is uniform at all points.
  • The slide is frictionless.

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