# 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.
×