Question

Мяч брошен вертикально вверх со скоростью 16 метров в секунду . На какой высоте его кинетическая энергия будет равна потенциальной?

Answer 1

Дано:

v=16м/c

h(Eп=Ек)-?

Решение:

Еп1+Ек1=Еп2+Ек2

Но так как на этой высоте кинетическая энергия равна потенциальной, то получится следующее6

Еk=2Еп

mv^2/2=2mgh

v^2/2=2gh

v^2=4gh

h=v^2/4g

h=256/40=6,4м

Ответ: 6,4 м

Answer 2

Calculation of Kinetic and Potential Energy

To determine the height at which the kinetic energy of the ball is equal to its potential energy, we need to calculate both energies and set them equal to each other.

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

Kinetic Energy (KE) = (1/2) * mass * velocity^2.

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

Potential Energy (PE) = mass * gravity * height.

Given: - Initial velocity (v) = 16 m/s - Mass (m) = unknown - Gravity (g) = 9.8 m/s^2

Let's calculate the kinetic energy first:

KE = (1/2) * m * v^2

Now, let's calculate the potential energy:

PE = m * g * h

To find the height (h) at which the kinetic energy is equal to the potential energy, we can set the two equations equal to each other and solve for h:

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

Simplifying the equation:

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

Solving for h:

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

Now, let's substitute the given values into the equation to find the height:

h = (1/2) * (16 m/s)^2 / (9.8 m/s^2)

Calculating the height:

h ≈ 13.06 meters

Therefore, the height at which the kinetic energy of the ball will be equal to the potential energy is approximately 13.06 meters.

Please note that the mass of the ball was not provided in the question, so we cannot calculate the exact value of the height without knowing the mass.