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