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A 1000kg roller coaster has a velocity of 10 m/s as it crests a 40m hill. The track and coaster aremade out of miraculous materials so no mechanical energy is lost after this point! It drops to a dip of height 5m,then climbs to a height of 30m where a 250kg car disconnects with no loss in energy as the roller coaster creststhe hilltop.

(a) What is the total mechanical energy of the roller coaster/earth system at the 40m hilltop?

(b) What is the kinetic energy of the roller coaster at the 5m dip?

(c) What is the kinetic energy of the main part of the roller coaster at the 30m crest (after the car falls off)?

(d) What is the kinetic energy of the individual car at the 30m crest?

(e) Now let's say that at the 30m hill, the disconnected car is stopped by electric emergency brakes. Themain part crashes into and connects with an articulated 500kg car that is going 2m/s slower. How farup the next hill can this new combination of cars go?

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