Mathematics

Posted: August 12th, 2013

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WebQuest Part

Question 1a

The first roller coaster built in the United States was designed by John G. Taylor in 1873. He was issued a patent in 1872 for an improvement of elevated railways, as they were known at the time. It was built in Savin Rock in West Haven, Connecticut.

In 1884, LaMarcus Thompson obtained a patent to build his switchback railway in Coney Island, New York.

The following year, 1885, saw Charles Alcoke obtain a patent to construct a serpentine railway in Coney Island.

Question 1b

The coasters made during this era were constructed entirely of wood. The switchbacks consisted of a car with wheels to aid in the switching when the ride reached on end of the rail.

Question 1c

Steel is the modern choice for roller coasters because of its malleability compared to wood. The use of steel ensured that these coasters have intricate turns, loops and bends to give a more thrilling experience to the rider.

Question 2 (Goldish, 25-39)

 Name of Theme Park Location in U.S. Name of Roller Coaster Height Length Speed (rate) Duration of ride (time) Average acceleration Six Flags New England Agawam, Massachusetts Bizarro 208 feet 5, 400 feet 77 miles per hour 47.82 seconds 1.44 meters/ squared seconds Six Flags Great Adventure Jackson, New Jersey Kingda Ka 456 feet 3 118 feet 128 miles per hour 16.61 seconds 7.28 meters/ squared seconds Six Flags Fiesta Texas San Antonio, Texas Superman: Krypton Coaster 168 feet 4, 025 feet 70 miles per hour 39.20 seconds 1.6 meters/ squared seconds Cedar Point Sandusky, Ohio Top Thrill Dragster 429 feet 2, 800 feet 120 miles per hour 15.91 seconds 6.74 meters/ squared seconds Kings Dominion Doswell, Virginia Volcano, The Blast Coaster 155 feet 2, 757 feet 70 miles per hour 26.85 seconds 2.33 meters/ squared seconds

Question 3

Time = distance/speed (Larson et al., 156-165)

a)      Speed in feet/second = (77 miles/1 hour)(5280 feet/1 mile)(I hour/3600 seconds)

= 122.933 feet/second

Time = 5400 feet/ (122.93 feet/second)

= 47.82 seconds

b)      Speed in feet/second = (128 miles/1 hour)(5280 feett/1 mile)(1 hour/3600 seconds)

= 187.73 feet/second

= 3118 feet/ (187.73 feet/second)

Time = 16.61 seconds

c)      Speed in feet/second = (70 miles/1 hour)(5280 feett/1 mile)(1 hour/3600 seconds)

= 102.67 feet/second

Time = 4025 feet/ (102.67 feet/second)

= 39.20 seconds

d)      Speed in feet/second = (120 miles/1 hour)(5280 feett/1 mile)(1 hour/3600 seconds)

= 176 feet/second

Time = 2800 feet/ (176 feet/second)

= 15.91 seconds

e)      Speed in feet/second = (70 miles/1 hour)(5280 feett/1 mile)(1 hour/3600 seconds)

= 102.67 feet/second

Time = 2757 feet / (102.67 feet/second)

= 26.85 seconds

Question 4

Acceleration = 2s/ t squared (Larson et al., 156-165)

Where: s = distance in meters

t = time in seconds

a)      Distance in meters = 5400 feet (1 meter/3.281 feet)

= 1645.84 meters

Acceleration = (2*1645.84)/ (47.82*47.82)

= 1.44 meters/ squared seconds

b)      Distance in meters =3118 feet (1 meter/3.281 feet)

= 950.32 meters

Acceleration = (2*950.32)/ (16.61*16.61)

= 7.28 meters/ squared seconds

c)      Distance in meters =4025 feet (1 meter/3.281 feet)

= 1226.76 meters

Acceleration = (2*1226.76)/ (39.20*39.20)

= 1.6 meters/ squared seconds

d)      Distance in meters =2800 feet (1 meter/3.281 feet)

= 853.4 meters

Acceleration = (2*853.4)/ (15.91*15.91)

= 6.74 meters/ squared seconds

e)      Distance in meters =2757 feet (1 meter/3.281 feet)

= 840.29 meters

Acceleration = (2*840.29)/ (26.85*26.85)

= 2.33 meters/ squared seconds

Question 5

 Height of the 1st Hill Shape of the First Hill The Exit Path Height of the 2nd Hill The Loop Results Trial 1 40 meters (131 feet ) Angled slope Medium slope 50 meters ( 164 feet ) No loop Trial 2 60 meters (197 feet) Obtuse  slope Angled slope 30 meters ( 98 feet ) Perfect circle Trial 3 80 feet ( 262 feet ) Slope Low slope 70 meters ( 230 feet ) elliptical

Explanation

The first trial was not fun nor was it safe. The first hill was too low to build momentum. The angled hill was dangerous as the return is a flat horizontal that is not safe. Possibility of a crash is increased with the shape of this coaster course. The ending of the ride is boring with no loop.

The second trial was more dangerous because of the choice of an obtuse first hill, which would set the coaster airborne then have a crash landing. The circular loop is hazardous as a successful completion of such a loop is yet to occur.

The third trial was successful. The shape of the initial and second hill ensured that the ride acquired more velocity. The elliptical loop is the safest kind of loop. The ride was both fun and safe as the choices led to an increased velocity for maximum fun.

Conclusion

1. The trill factor of the coaster was a main attraction. The novelty of the invention and the association with foreign royalty did a lot to attract curious crowds in the 1800s.
2. The first roller coasters were made of wood. Since then they have been constructed with steel. The cars have been made more comfortable and safe. The height of the coasters has increased to great heights. The lengths have also increased to encompass loops and inverted turns. The trill factor has instigated most of these innovations.
3. The Six Flags Great Adventure amusement park has two great roller coaster rides: the Kingda Ka that is the tallest steel coaster in the US, and the El Toro that is the best wooden roller coaster in the US. Others include Millennium Force in Cedar Point, Volcano in Kings Dominion that is the tallest inversion coaster in the world, and The Beast in Kings Island, which is the longest wooden coaster in the world.
4. The speed of the roller coaster should be great enough to overcome the first hill. The shape of the first hill determines the overall acceleration of the coaster in subsequent loops and hills. The acceleration of the ride should be gradual with the ride having the greatest acceleration at the middle and slowly coming to a stop at the end of the ride (Rau, 56).
5. The Kingda Ka is 3118 feet long, with a speed of 128 miles per hour the ride takes 16.61 seconds from start to finish. The Top Thrill Dragster at 2800 feet reaches a top speed of 120 miles per hour and the entire ride takes 15.91 seconds.
6. The acceleration is the rate at which the speed changes with time. The acceleration of the roller coaster ride should increase gradually with the loops and drops having the greatest acceleration (Pople, 181-192). This gives the partaker of the ride a feeling of a strong gravitational pull working against inertia felt as “butterflies in the tummy”, which makes the ride such a thrilling experience.

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