Question

Тело брошено вертикально вверх со скоростью 20 м/с. На какой высоте от точки бросания кинетическая энергия тела будет равна потенциальной?

Answer 1

Считаем за нулевой уровень - уровень бросания тела вверх

в момент бросания, тело обладает только кинет.энергией
E=Ek=mv²/2

на определенной высоте, тело обладает как кинет, так и потенц. энергией, по условие на этой высоте они равны
E= Ek+Ep=mu²/2 + mgh=2mgh

по ЗСЭ
mv²/2 =2mgh
h=v²/(4g)=400/40=10м

Answer 2

Calculation of the Height at which the Kinetic Energy is Equal to the Potential Energy

To determine the height at which the kinetic energy of the body is equal to the potential energy, we need to equate the two energies and solve for the height.

Let's assume the mass of the body is m and the initial velocity is v. The kinetic energy (KE) of the body is given by the formula KE = (1/2)mv^2, and the potential energy (PE) is given by the formula PE = mgh, where g is the acceleration due to gravity and h is the height.

Equating the two energies, we have:

(1/2)mv^2 = mgh

We can cancel out the mass m from both sides of the equation:

(1/2)v^2 = gh

Now, we can solve for the height h:

h = (1/2)v^2 / g

Given that the initial velocity v is 20 m/s, we need to know the value of the acceleration due to gravity g to calculate the height. The value of g is approximately 9.8 m/s^2 on Earth.

Substituting the values into the equation, we get:

h = (1/2) * (20 m/s)^2 / 9.8 m/s^2

Simplifying the equation, we find:

h ≈ 20.41 meters

Therefore, the height at which the kinetic energy of the body will be equal to the potential energy is approximately 20.41 meters above the point of release.

Please note that this calculation assumes no air resistance and a constant value of acceleration due to gravity.