Find the maximum height to which a body weighing 1 kg can rise, thrown vertically upward at a speed of 40 m / s.

Find the maximum height to which a body weighing 1 kg can rise, thrown vertically upward at a speed of 40 m / s. At what h will the speed be equal to 20m / s? What is Ep and Eк equal to at all heights?

m = 1 kg.

g = 10 m / s2.

V0 = 40 m / s.

V = 20 m / s.

hmax -?

h -?

Ep -?

Ek0 -?

Kinetic Ek and potential energy En are determined by the formulas: Ek = m * V2 / 2, En = m * g * h.

When the body moves, the law of conservation of total mechanical energy is valid.

At the moment of throwing, the total mechanical energy E consists only of kinetic energy: E = Ek0 = m * V02 / 2.

Ek0 = 1 kg * (40 m / s) 2/2 = 800 J.

At the maximum height hmax, the total mechanical energy will be added only from the potential energy: E = m * g * hmax = Ek0.

hmax = Ek0 / m * g.

hmax = 800 J / 1 kg * 10 m / s2 = 80 m.

Ek0 = m * g * h + m * V2 / 2.

h = (Ek0 – m * V2 / 2) / m * g.

h = (800 J – 1 kg * (20 m / s) 2/2) / 1 kg * 10 m / s2 = 60 m.

En = m * g * h.

Ep = 1 kg * 10 m / s2 * 60 m = 600 J.

Ek = 1 kg * (20 m / s) 2/2 = 200 J.

Answer: hmax = 80 m, h = 60 m, Ep = 600 J, Ek = 200 J.