A 37 kg child on roller skates, initially at rest, rolls 2.0 m down an incline at an angle of 17.0 degrees with the horizontal. If there is no friction between incline and skates, what is the kinetic energy of the child at the bottom of the incline?

As the child starts from rest and rolls down on the incline, the potential energy of the child decreases due to decrease in the height. This drops in potential energy appears as an increase in kinetic energy of the child as it gains speed. hence kinetic energy gained by the child at the bottom is same as the potential energy of the child at the top.

[tex]m[/tex] = mass of the child = 37 kg

[tex]L[/tex] = length of the incline surface = 2.0 m

[tex]\theta[/tex] = angle of the incline from the horizontal = 17 deg

[tex]K[/tex] = kinetic energy of the child at the bottom

height of the incline surface is given as

[tex]h = L Sin\theta\\h = (2.0) Sin17.0\\h = 0.585 m[/tex]

[tex]PE[/tex] = Potential energy of the child at the top

Potential energy of the child at the top of incline is given as

[tex]PE = mgh \\PE = (37) (9.8) (0.585)\\PE = 212.12 J[/tex]

Using conservation of energy

Kinetic energy at the bottom = Potential energy at the top

[tex]K = PE\\K = 212.12 J[/tex]