The body moves at a speed of 20m / s. At what height are its kinetic and potential energies equal?

The kinetic energy of a body is calculated by the formula: Eк = mv² / 2, where m is the mass of the body, v is its speed.

The formula of its potential energy: Ep = gmh, where g is the acceleration of gravity, m is the mass of the body, h is its height above the earth’s surface.

Let’s compose an equation from which we can calculate the required value (height): Eк = Ep – mv² / 2 = gmh.

Let’s substitute in it the values ​​we have: (m * (20 m / s) ²) / 2 = 9.8 m / s² * m * h.

Simplifying the expression, we get – 200 (m / s) ² = 9.8 m / s² * h. Or – h = 200 / 9.8 = 20.4 m (rounding the infinite fraction to one decimal place).

Answer: at a height of 20.4 m near a body moving at a speed of 20 m / s, the kinetic and potential energies will be equal.