Part A.
Refer to the diagrams shown below.
Define
KE = kinetic energy
PE = potential energy
Also,
m = 15 kg, the mass of the rollercoaster
h = 10 m, the height of the ramp.
Part B.
When the rollercoaster begins to roll down, its initial velocity is zero.
Therefore the rollercoaster has
KE = 0
PE = mgh = (15 kg)*(9.8 m/s²)*(10 m) = 1470 J
Answer: The initial PE = 1470 J
Part C.
Answer: The initial KE = 0
Part D.
Assume that frictional forces and air resistance may be ignored.
At the bottom of the ramp, the rollercoaster has
PE = 0
KE = (1/2)*m*v² = 0.5*(15 kg)*(v m/s)² = 7.5v² J
Because energy losses are ignored, the conservation of energy requires that
7.5v² = 1470
v² = 196
v = 14 m/s
Answer: 14 m/s
