A stone thrown from the surface of the Earth at a speed of 10 m / s. Determine the height to which the stone flew.

According to the law of conservation of energy:
Eк1 + Eп1 = Eк2 + Eп2, where Eк1, Eп1 – energy at the moment of throw; Eк2, Ep2 – energy at max. height.
At max. height: V = 0, Eк2 = 0.
At the beginning of the stone throw: h = 0 m, Ep1 = 0 m.
Eк1 = Ep2; Eк1 = (m * V0 ^ 2) / 2, where V0 is the initial velocity of the stone (V = 10 m / s); Ep2 = m * g * h, where g is the acceleration of gravity (assumed g = 10m / s ^ 2).
(m * V ^ 2) / 2 = m * g * h.
h = (V ^ 2) / 2g = 100/2 * 10 = 5 m.
Check: m = ((m / s) ^ 2) / (m / s ^ 2) = (m ^ 2 * s ^ 2) / (m * s ^ 2) = m.
Answer. The stone will reach a height of 5 m.