At what altitude the kinetic energy will be 2 times greater than the potential if the body

At what altitude the kinetic energy will be 2 times greater than the potential if the body is thrown vertically upward at a speed of 72 km / h.

Given:

v0 = 72 km / h = 20 m / s – the initial speed with which the body was thrown;

Ek = 2 * Ep – kinetic energy is 2 times more potential.

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine the height h (meters) at which the condition Ek = 2 * Ep is satisfied.

According to the law of conservation of energy:

Eк0 = Ek + Ep;

Eк0 = 2 * Ep + Ep;

Eк0 = 3 * Ep;

m * v0 ^ 2/2 = 3 * m * g * h;

v0 ^ 2/2 = 3 * g * h;

h = v0 ^ 2 / (6 * g) = 20 ^ 2 / (6 * 10) = 400/60 = 6.7 meters.

Answer: the kinetic energy will be 2 times the potential at a height of 6.7 meters.