Question

At the beginning of a roller coaster ride, the car is lifted to the top of a large hill and
released. The speed of the car at the top of the hill is small, so we will assume it to be
zero. The car rolls freely down this hill and reaches its maximum speed at the bottom.
If the roller coaster were frictionless, mechanical energy would be conserved… Ei = Ef.
Showing all terms for potential and kinetic energy, set up the conservation of mechanical
energy for this situation…





yi

vf







Solve this relationship for the maximum speed of the car, vf, in terms of height, yi .

Answer 1

At top of hill:
KE + PE = mg*h
0 + PE = mg*h
PE = mg*h

At bottom of hill:
KE + PE = mg*h
KE + 0 = mg*h
KE = mg*h = 0.5m*V^2
0.5m*V^2 = mg*h
V^2 = 2g*h
V = Sqrt(2g*h).
V = Sqrt(19.6*h).

Sqrt means Square root.