Question

Мяч брошен вертикально вверх со скоростью v=40 м/с. На какой высоте h (м) кинетическая энергия мяча составляет k=2/3 часть от его потенциальной энергии?

Answer 1

mv^2 /2 = mgh + 2mgh/3

h = 3v^2 /(10g) = 4800/100 = 48 

Ответ: 48 м.

Answer 2

Закон сохранения энергии

mv0^2/2=mgh+mv^2/2

Сокращаю массу

v0^2/2=gh+v^2/2    (*)

Составляю уравнение к условию: кинет энергия на определ высоте равна 2/3 потенц энергии

mv^2/2=2/3(mgh)

v^2/2=2gh/3

3v^2=4gh

v^2=4gh/3

  Подставляю это выражение квадрата скорости в уравнение (*)

v0^2/2=gh+4gh/3

Привожу к общему знаменателю

v0^2/2=(3gh+4gh)/3

3v062=14gh

h=3v0^2/14g=3*40м/с*40м/с/(14*9.8м/с*с)=3*1600/140=34.3м

Answer 3

Calculation of the Height at which the Kinetic Energy of the Ball is 2/3 of its Potential Energy

To determine the height at which the kinetic energy of the ball is 2/3 of its potential energy, we can use the equations for kinetic and potential energy.

The kinetic energy of an object is given by the equation:

KE = (1/2)mv^2 where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

The potential energy of an object at a certain height h is given by the equation:

PE = mgh where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height.

We are given that the ball is thrown vertically upwards with a velocity of v = 40 m/s. We need to find the height at which the kinetic energy is 2/3 of the potential energy.

Let's assume the mass of the ball is m = 1 kg for simplicity.

Using the equation for kinetic energy, we can calculate the kinetic energy of the ball:

KE = (1/2)mv^2 = (1/2)(1 kg)(40 m/s)^2 = 800 J

Now, we need to find the height at which the potential energy is 2/3 of the kinetic energy.

Let's substitute the values into the equation for potential energy:

PE = mgh = (1 kg)(9.8 m/s^2)h = 9.8h J

We can set up the equation:

(2/3)PE = (2/3)(9.8h J) = 800 J

Simplifying the equation:

(2/3)(9.8h J) = 800 J

6.53h = 800

h ≈ 122.5 meters

Therefore, the height at which the kinetic energy of the ball is 2/3 of its potential energy is approximately 122.5 meters.

Please note that the calculations assume a mass of 1 kg for simplicity. The actual mass of the ball may vary, but the height at which the kinetic energy is 2/3 of the potential energy will remain the same.