At what height will the body be falling freely without initial speed from a height of 35m

At what height will the body be falling freely without initial speed from a height of 35m when its speed reaches a speed of 20m / s.

Given:

H = 35 meters – the height from which the body falls;

v = 20 m / s – body speed at a certain height H1;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine the height H1 (meter).

According to the law of conservation of energy, the potential energy of a body at height H will be equal to the sum of kinetic and potential energies at height H1:

m * g * H = m * g * H1 + m * v ^ 2/2;

g * H = g * H1 + v ^ 2/2;

2 * g * H = 2 * g * H1 + v ^ 2;

2 * g * H1 = 2 * g * H – v ^ 2;

H1 = (2 * g * H – v ^ 2) / (2 * g) = H – v ^ 2 / (2 * g);

H1 = 35 – 20 ^ 2 / (2 * 10) = 35 – 400/20 = 35 – 20 = 15 meters.

Answer: the body will reach a speed of 20 m / s at a height of 15 meters.