The hyperbola can be used to mathematically model part of the track of a roller coaster ride.Y=23/(1050-5x ) models such a ride.

a) Explore the safety aspects of travelling as a passenger inside the curved section, of this model over the domain 174m<x<208m. consider the centripetal acceleration experienced by the rider.

b) Derive a model of the form Y=A/(B-Cx) which, ensures a thrilling but safe journey for the rider while travelling inside the curved part of the ride. Justify that the rider is experiencing the safest maximum acceleration on this part of the ride. Specify the age group for which your ride is designed.

Assumptions:

• The train of the roller coaster travels 45m/sec in the horizontal direction(x-direction) before it enters the curved part of the journey

• The radius of curvature=1/5 (track length prior to entering curved section)

• 160m<=(horizontal section of track + radius of curvature)<= 210m

Hints:

• you may restrict the domain for mathematical modelling purpose

• the use of significant fugures should reflect that the equation will only be a mathematical model

g’s are measured as (centripetal acceleration(m/sec2)/9.8m/sec2). The acceleration due to gravity on earth is 9.8m/s2

[g’s felt by the rider = (centripetal acceleration in g’s)+1] at the bottom of a loop

Most roller coasters keep the g’s felp under 5g’s on an inside loop or the bottom of a dip after a hill. For safety purpose we will restrict the centripetal acceleration to below 4.5g’s.