Arollercoaster car with a mass of 15 kg rolls down a ramp that is 10.0 meters tall. a) draw a sketch of the situation. b) what is the initial potential energy of the rollercoaster car? c) what is the initial kinetic energy of the rollercoaster car? d) calculate the speed of the roller coaster at the bottom of the ramp.

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

The initial PE = 1470 J

Part C.
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

14 m/s