In: Physics
1. Kingda Ka is one of Six Flags famous roller coasters. It does not have a running engine. A hydraulic launcher “shoots” the roller coaster with an initial velocity of 57 m/s and relies on the conservation of energy to take care of the rest until the end of the ride. The first hill that the roller coaster goes over is 127 meters above the original launch height. After the coaster returns to the original launch height, it goes over a second hill of 39 meters above the launch height, before slowly coming to a stop. The mass of the coaster with its riders is approximately 2200 kg. Assume no air resistance and no friction for the time being and its launch height to be 0m.
a. How much potential energy does the coaster, with its riders, have right after it is shot out by the hydraulic launcher?
b. Determine the kinetic energy a coaster, with its riders, has right after it is shot out by the hydraulic launcher.
c. Determine the potential energy a coaster, with its riders, has at the top of the 127m hill?
d. Determine the kinetic energy a coaster, with its riders, has at the top of the 127m hill?
e. At what speed does the coaster, with its riders, travel at top of the first hill?
f. Determine the potential energy a coaster, with its riders, has at the top of the 39m hill?
g. Determine the kinetic energy a coaster, with its riders, has at the top of the 39m hill?
h. At what speed does the roller coaster travel over the second hill?
i. What is the slowest speed that the roller coaster must be launched at in order to get it over the first hill? (Again, neglect friction and air resistance.)