The body is thrown from the surface of the earth vertical to the top at a speed of 30 m / s.

The body is thrown from the surface of the earth vertical to the top at a speed of 30 m / s. Determine at what height the speed of the body will be 10 m / s

Given:

v0 = 30 meters / second – the speed at which the body was thrown;

v1 = 10 meters / second – required body speed;

g = 10 Newton / kilogram – acceleration of gravity.

It is required to determine h (meter) – at what height the body’s velocity will be equal to v1.

To determine the speed, it is necessary to use the following equality (according to the law of conservation of energy):

Ekin (at the surface of the earth) = Epot (at a height h) + Ekin (at a height h);

m * v0 ^ 2/2 = m * g * h + m * v1 ^ 2/2, where m is body weight;

v0 ^ 2/2 = g * h + v1 ^ 2/2;

v0 ^ 2 = 2 * g * h + v1 ^ 2;

2 * g * h = v0 ^ 2 – v1 ^ 2;

h = (v0 ^ 2 – v1 ^ 2) / (2 * g) = (30 ^ 2 – 10 ^ 2) / (2 * 10) =

= (900 – 100) / 20 = 800/20 = 80/2 = 40 meters.

Answer: at a height of 40 meters.