With what initial speed was the body thrown vertically upward, if at a height of 10 m

With what initial speed was the body thrown vertically upward, if at a height of 10 m its kinetic and potential energies were the same?

Given:

Ekin = Epot – at the height h the kinetic and potential energies of the body are equal;

h = 10 meters – body height;

g = 10 meters per second squared – the acceleration of gravity.

It is required to determine v0 (m / s) – with what initial speed the body should be thrown.

According to the law of conservation of energy:

Ekin (near the surface of the earth) = E (potential at height h) + E (kinetic at height h);

Since, according to the condition of the problem at a height h, the kinetic and potential energies are equal, then:

Ekin (at the surface of the earth) = 2 * E (potential at a height h);

m * v0 ^ 2/2 = 2 * m * g * h, where m is body weight;

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

v0 = (4 * g * h) ^ 0.5 = (4 * 10 * 10) ^ 0.5 = 400 ^ 0.5 = 20 m / s.

Answer: the body must be thrown upward at a speed equal to 20 m / s.