How Calculus applies in Roller Coasters

                                                                           Yuqi Zheng

                                                                          Yuchen Zheng

                                                                           Zi Ang Wang

 Do you know that roller coasters have no engine?

Since the roller coasters have no engine, how can they go so fast and make people scream?

• At the beginning of the ride, the car is pulled to the top of the first hill. Then, it completes the whole ride on its own. The first hill is always the highest one(unless you listen for more clicking sounds which are from motorized chain that pulls the car). So the first hill has the largest large amount of gravitational potential energy which is enough to take you to the end of the ride.  
• The roller coaster is pulled down by gravity. What drives the roller coaster is the conversion of the potential to kinetic energy. The energy changes from stored energy to moving energy.
• When the car goes to the end, the compressed air break stops the car. 

Do you know why the roller coasters are safe even they don't have engine?

It's because of CALCULUS. The speed, acceleration, slope, and maximum and minimum height of a roller coaster are all found through the applications of calculus.

• Engineer predict the speed of the roller coaster at a given height and slope with the help of physics by using calculus.
• Calculus can make sure the safety of the roller coaster speed and determine how fast it is going at a certain point.
• Calculus is also an important method to determine the maximum and minimum  height  the roller coaster can go.

Without the application of CALCULUS, even a roller coaster has a lot of potential energy, it still would not be able to operate safely.