Class notes
Engineering a rollercoaster
- Course
- MHF4U
- Institution
- 12th Grade
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1) Name: Leviathan, Location: Canada’s wonderland in Vaughn, Toronto, Built: February 2012,Physical characteristics: This rollercoaster exceeds a height of 91.5 meters. The ride is 1,672
meters long, 93.3 meters tall and has a speed of 148 km/h. Once the train leaves the station, the
ride trunks 180 degrees to the right leading to the track to climb then drop. Once the ride reaches
the top, it drops to the ground at an angle of 80 degrees. After the first drip, the train goes
through a 30 meter tunnel then curves up into a 50 meter tall tunnel which is located to the right
(Kiddle, 2023). This is followed by another that enters a hill and then turns left at a high speed.
The exit of this high speed leads to a 56 meter tall camelback then a 44 meter tall 115 degree
turn. After leaving this turn, the train approaches a high speed curve then approaches another
camelback finally leading to the station (Kiddle, 2023).
2) How do roller coasters work? The reason the roller coaster goes up on the tracks is to build a
storage of potential energy. Potential energy is called energy of position and this concept is
simple. As the coaster goes high in the air, gravity can pull the coaster down a greater distance.
Once the roller coaster starts coming down, the potential energy that was stored gets converted
into kinetic energy with the help of gravity (Howstuffworks, 2023). Gravity applies a downward
force on the cars and the tracks help by controlling the way the cars fall. If the slope of the track
is down, gravity pulls the tracks towards the ground. If the slope of the track is up, gravity
supplies a downward force on the track so it goes up slowly. This process continues for the rest
of the maneuvers the track encounters (Howstuffworks, 2023).
4)
State equation Degree of function Domian and range Symmetry
y=1.5 First {0≤ 𝑥 ≤ 6. 75} Odd
1
y= 2 (𝑥 − 7. 1) +
2 Second {6.30 ≤ 𝑥 ≤ 60} Even
{0≤ 𝑦 ≤ 57}
1.45
y= -1.75 Second {6 ≤ 𝑥 ≤ 25} Even
2 {0≤ 𝑦 ≤ 57}
(𝑥 − 21. 35) +80
1 2 Second {25≤ 𝑥 ≤ 29. 56} Even
y= 23 x(𝑥 − 32) +5
1 2 Fourth {29.56 Even
y= 76 (𝑥 − 32. 01) ≤ 𝑥 ≤ 31. 353}
2
(𝑥 − 40) +4.1
y= 2
1 Second {31.353≤ 𝑥} Even
{y≤ 42. 5}
2
(𝑥 − 33. 6) + 2
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