An 800.0 kg roller coaster car is at rest at the top of a 95 m hill. It rolls down the first drop to a height of 31 m. When it travels to the top of the second hill, it is moving at 28 m/s. It then rolls down the second hill until it is at ground level.

Question

What is the kinetic and potential energy at the top and bottom of each hill?

Answer 1

They presumably want to to assume total mechanical energy (kinetic + potential) is constant, even though that is not the case.

At the top of the 95 m hill, all of the energy is potential, and equals
M g H = 744,800 J. Use the height or velocity at the other location, and the total energy (748,800 J) , to determine kinetic and potential energies

Answer 2

1.
PE1 = mgh1 = 800•9.8•95 =744800 J.
KE1=0.
Total E1 = PE1+ KE1=744800 J.
2.
PE2 = 800•9.8•31=243040
PE1= PE2+KE2
KE2 = PE1- PE2 =
=744800 - 243040=501760 J.
Total E2 = PE2+ KE2=744800 J.
3.
KE3 =mv²/2= 800•(28)²/2 =313600 J.
PE3 =744800-313600 = 431200 J.
Total E3 = PE3+ KE3=744800 J.
4.
PE4=0.
KE4 = 744800 J.
Total E4 = PE4+ KE4=744800 J.