Determine from what height the body submitted, if at a height of h = 10 m its speed is U = 10 m / s.

Determine from what height the body submitted, if at a height of h = 10 m its speed is U = 10 m / s. Neglect the movement resistance, take the coefficient g equal to 10 N / kg.

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 reaching a height of 10 m.
Since at the beginning of the fall of the body the initial velocity was equal to zero, then Eк1 = 0.
Then:
Ep1 = Ec2 + Ep2, where Ep1 = m * g * h1, Ep2 = m * g * h2, Ec2 = (m * V ^ 2) / 2 (g = 10 m / s ^ 2, h2 = 10 m, V = 10 m / s).
m * g * h1 = m * g * h2 + (m * V ^ 2) / 2.
h1 = ((g * h2 + (V ^ 2) / 2)) / g = (10 * 10 + (10 ^ 2) / 2) / 10 = (100 + 100/2) / 10 = (100 + 50) / 10 = 15 m.
Answer. The body fell from a height of 15 m.