what is the height of an inclined plane in order that a circular disk will roll from rest to the bottom with a final velocity of 20 m/s?

30 m

Explanation:

Potential energy = kinetic energy + rotational energy

PE = KE + RE

mgh = ½ mv² + ½ Iω²

For a disk, I = ½ mr².  For rolling without slipping, ω = v/r.

mgh = ½ mv² + ½ (½ mr²) (v/r)²

mgh = ½ mv² + ¼ m v²

mgh = ¾ m v²

gh = ¾ v²

h = 3v² / (4g)

h = 3 (20 m/s)² / (4 × 10 m/s²)

h = 30 m

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.