Here are the steps to solve the roller coaster energy problems:
1. PE at point A = mgh = (20 kg)(10 m/s^2)(250 m) = 50,000 J
2. KE at point A = 0 J (velocity is 0 m/s at the top)
3. ME at point A = PE + KE = 50,000 J + 0 J = 50,000 J
4. KE at point B = 1/2mv^2 = 1/2(20 kg)(200 m/s)^2 = 40,000 J
5. ME at point C = ME is conserved. ME at point A was 50,000 J.
6. PE at