Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

Design a BIG waterslide

One of the largest waterslides in the world is the Insano, located in a park near the city of Fortaleza in Brazil. It's ... pretty big.


Image courtesy of AmazingPlaces.com

Let's analyze the motion of a person descending this device. We'll make a few simplifying assumptions:

Our model doesn't look quite as pretty -- no palm trees or view of the Atlantic -- but it will simplify the analysis.

The Insano's dimensions are roughly H = 41 m and L = 13 m, yielding an angle of θ = 72.4 degrees.. A standard adult human being has a mass of m = 60 kg. Consider a person who dares to enter the slide.

  1. What is the net force on the human? Express in unit-vector notation.
  2. What is the acceleration of the human?
  3. How long will it take to descend from the top to the bottom of the ride? In other words, how long will the slide last?
  4. How fast will the human be travelling at the bottom? Express in both m/s and miles per hour.

Now, at the bottom of the slide, riders shoot into a pool of water to slow down. Amusement parks have learned (the hard way) that accelerating people at more than about three gees is a very bad idea: it leads to injuries and, even worse, lawsuits. So, suppose that the pool is designed to decelerate riders at exactly a = -2 gees = -19.6 m/s2.

  1. How long should the pool be, based on physics?
  2. If you were designing the pool, how long would you make it? Why?

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.