# The ball is thrown from the surface of the earth vertically upwards at a speed of 10 m / s. At what height will the potential

**The ball is thrown from the surface of the earth vertically upwards at a speed of 10 m / s. At what height will the potential energy of the sphere be 1.5 times greater than the kinetic one?**

V0 = 10 m / s.

g = 9.8 m / s2.

n = 1.5.

En = n * Ek.

h -?

According to the law of conservation of total mechanical energy, the total mechanical energy of the ball E remains unchanged: E = const.

At the initial moment of time, the total mechanical energy E consists only of kinetic energy: = m * V0 ^ 2/2.

At height h, the body has both kinetic Ek and potential energy En, the total mechanical energy E will be their sum: E = En + Ek = En + En / n.

En = m * g * h.

m * V0 ^ 2/2 = m * g * h + m * g * h / n.

V0 ^ 2/2 = g * h + g * h / n.

h = V0 ^ 2/2 * g * (1 + 1 / n).

h = (10 m / s) ^ 2/2 * 9.8 m / s ^ 2 * (1 + 2/3) = 3 m.

Answer: at a height of h = 3 m Ep = 1.5 * Ek.