A stone is thrown from the surface of the Earth vertically upwards with a speed u = 10m / s.

A stone is thrown from the surface of the Earth vertically upwards with a speed u = 10m / s. Determine at what height the kinetic energy of the stone will decrease by 5 times.

According to the law of conservation of energy:
Eк1 + Eп1 = Eк2 + Eп2, where Eк1 and Eп1 – energy at the beginning of movement; Eк2, Eп2 – energy at the moment of decreasing kin. energy 5 times.
Since at the beginning of the throw h = 0, then Ep1 = 0.
Eк1 = Eк2 + Eп2, where Eк2 = 0.2Eк1 (kinetic energy decreased 5 times).
Eк1 = 0.2Eк1 + Ep2, Ep2 = 0.8Eк1, where Ep2 = m * g * h (g = 10 m / s ^ 2), Eк1 = (m * V ^ 2) / 2 (V = 10 m / from).
m * g * h = 0.8 * (m * V ^ 2) / 2;
h = 0.4 (V ^ 2) / g = 0.4 * (10 ^ 2) / 10 = 4 m.
Answer. The kinetic energy will decrease by 5 times at a height of 4 m.