01 The Kingda Ka roller coaster at Six Flags Great Adventure (NJ) accelerates fr
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Question
01 The Kingda Ka roller coaster at Six Flags Great Adventure (NJ) accelerates from zero to 128 mph in 3.5 seconds and hits a maximum height of 456 feet. Calculate the total kinetic energy of a 135 lb rider at the maximum launch speed Calculate the total potential energy of the same rider at the max elevation (assume launch elevation is datum) Determine the percentage of the K.E. dissipated if the rider reaches the max elevation at a speed of 35 mph. Does your answer make sense-why or why not? a. b. c.Explanation / Answer
a) Given : Maximum speed is 128mph = 57.22 m/s ( 1 mile = 1.609Km)
Mass of the rider = 135lb = 61.235 kgs (Since 1 lbs = 0.4536 Kg)
Kinetic energy = mv2/2 = 61.235 kg * (57.222 m2/s2)/2 = 100245.63= 1.003 x 105 Joules.
b) Given Maximum height = 456 feet = 139 m
Mass of the rider = 135lb = 61.235 kgs (Since 1 lbs = 0.4536 Kg)
Potential Energy = mgh = 61.235 * 9.8 *139 = 83414.317 Joules = 8.34 x 104 Joules.
c) Velocity of the rider at the maximum elevation=35 mph = 15.6464 m/s
Kinetic energy of the rider at the maximum elevation = mv2/2 = 61.235 kg * (15.652 m2/s2)/2 = 14997.83 Joules =1.5 x 104 Joules.
Kinetic Energy Dissipated = 100245.63 - 14997.83 = 85247.8 Joules = 8.53 x 104 Joules
%Kinetic energy dissipated = (853247.8/100245.63) x 100 = 85.04%
Thus about 85% of the Kinetic energy has been dissipated during the journey,
But this is not actually dissipated but is stored as the Potential energy, since energy can be neither created nor destroyed.
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