Question on conservation of energy [closed]

Question

Problem:

The Top Thrill Dragster stratacoaster at Cedar Point Amusement Park in Ohio uses a hydraulic launching system to accelerate riders from 0 to 53.6 m/s (120 mi/hr) in 3.8 seconds before climbing a completely vertical 420-foot hill.

1. Jerome (m=102 kg) visits the park with his church youth group. He boards his car, straps himself in and prepares for the thrill of the day. What is Jerome's kinetic energy before the acceleration period?

2. The 3.8-second acceleration period begins to accelerate Jerome along the level track. What is Jerome's kinetic energy at the end of this acceleration period?

3. Once the launch is over, Jerome begins screaming up the 420-foot, completely vertical section of the track. Determine Jerome's potential energy at the top of the vertical section. (GIVEN: 1.00 m = 3.28 ft)

4. Determine Jerome's kinetic energy at the top of the vertical section.

5. Determine Jerome's speed at the top of the vertical section.

Answers:

1. $0 \,\mathrm{J}$

2. $1.47 \cdot 10^5 \,\mathrm{J}$

3. $1.28 \cdot 10^5 \,\mathrm{J}$

4. $1.9 \cdot 10^4 \,\mathrm{J}$

5. $19 \, \frac{\mathrm{m}}{\mathrm{s}}$

In the answer explanation, in order to get the answer to Part (4), you use the conservative forces equation (initial kinetic energy + initial potential energy = final kinetic energy + final potential energy).

The answer explanation also says that the answer to Part (2) is equal to the initial kinetic energy + initial potential energy. This means that the potential energy for Part (2) is zero, but doesn't that mean that the total mechanical energy for question a is zero (the track is level so height is 0, gravitational potential energy, or $mgh,$ would also equal $0$)? However, if the total mechanical energy is zero, that makes no sense.

Answer 1

I think you are getting confused here because the question has two "initial" periods. The first "initial" period is before acceleration takes place (let's call this P1), and the second "initial" period is after the acceleration takes place (let's call this P2). At time P1 it is true that the total mechanical energy is equal to 0 (given you define h=0 at the ground level). At time P2, it is no longer true that the total mechanical energy is equal to 0. The mechanical energy has increased because the hydraulics in the roller coaster has accelerated Jerome. The acceleration that occured between P1 and P2 has provided Jerome with the energy found in part b of the question. Then you use P2 as your "initial" values to do the rest of the problem.

P.S. Regarding this problem as having no friction (non-conservative forces) is problematic as that implies Jerome (and the coaster) still has a velocity going upwards at the top of the vertical section....which means Jerome + the coaster should shoot off the track!