# The stone falls without initial speed from a height of 6 meters from the surface of the earth.

The stone falls without initial speed from a height of 6 meters from the surface of the earth. At what height will the kinetic energy of the stone be 2 times its potential energy?

V0 = 0 m / s.

h0 = 6 m.

g = 10 m / s2.

Ek = 2 * Ep.

h -?

The potential energy of the stone, En, is determined by the formula: En = m * g * h.

The kinetic energy of the stone Ek is determined by the formula: Ek = m * V ^ 2/2.

According to the law of conservation of total mechanical energy: En0 = Ek + En.

Since according to the condition of the problem Ek = 2 * En, the formula for the law of conservation of the total mechanical energy will take the form: En0 = 2 * En + En = 3 * En.

m * g * h0 = 3 * m * g * h.

h = h0 / 3.

h = 6 m / 3 = 2 m.

Answer: at a height of h = 2 m from the surface, the kinetic energy of the stone will be 2 times its potential energy.

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