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? Neglect air resistance

Potential energy (in the Earth’s gravitational field) Ep = mgh, where m is the mass of the body, g is the acceleration of gravity (10 m / s ^ 2), h is the height of the body above the zero level (10 m).
Kinetic energy Ek = (mV ^ 2) / 2
From the conditions of the problem Ek1 = Ep.
According to the law of conservation of energy:
Ek0 = Ek1 + Ep = 2Ep = 2mgh = (mV ^ 2) / 2.
Hence: 4gh = V ^ 2; V ^ 2 = 400; V = 20 m / s.
Check: m / s = ((m / s ^ 2) * m) ^ 0.5 = (m ^ 2 / s ^ 2) ^ 0.5 = m / s.
Answer: the initial velocity of the body is 20 m / s.



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