1. Kingda Ka is one of Six Flags famous roller coasters. It doesnot have a running engine. A hydraulic launcher “shoots” the rollercoaster with an initial velocity of 57 m/s and relies on theconservation of energy to take care of the rest until the end ofthe ride. The first hill that the roller coaster goes over is 127meters above the original launch height. After the coaster returnsto the original launch height, it goes over a second hill of 39meters above the launch height, before slowly coming to a stop. Themass of the coaster with its riders is approximately 2200 kg.Assume no air resistance and no friction for the time being and itslaunch 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, hasright 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, hasat the top of the 127m hill?

e. At what speed does the coaster, with its riders, travel attop 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, hasat the top of the 39m hill?

h. At what speed does the roller coaster travel over the secondhill?

i. What is the slowest speed that the roller coaster must belaunched at in order to get it over the first hill? (Again, neglectfriction and air resistance.)