A heavy body slides on a smooth surface of an inclined plane. Determine its height at which

A heavy body slides on a smooth surface of an inclined plane. Determine its height at which the speed of the body in the lower position V = 2 m / s.

To find the height of a smooth surface, we will use the equality (we assume that there was no friction during sliding of a heavy body): Ek = Ep and m * V ^ 2/2 = m * g * h, whence h = V ^ 2 / 2g.

Constants and variables: V – speed in the lower position (V = 2 m / s); g – acceleration due to gravity (g ≈ 10 m / s2).

Calculation: h = V ^ 2 / 2g = 2 ^ 2 / (2 * 10) = 0.2 m.

Answer: A smooth surface is 0.2 m high.