Question

Определите, на какой высоте кинетическая энергия мяча, брошенного вертикально вверх со скоростью 16 м/с, равна его потенциальной энергии

Answer 1

По закону сохранения энергии
$Ek1=Ek2+Ep2$
$Ek2=Ep2$ по условию
$Ek1=2Ep1$
$\frac{mv ^{2} }{2} =2mgh$
$h= \frac{v ^{2} }{4g} = \frac{16*16}{4*10} =6.4m$ Ответ

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 a ball, thrown vertically upwards with a velocity of 16 m/s, is equal to its potential energy, we can use the equations for kinetic energy 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 (approximately 9.8 m/s^2), and h is the height.

To find the height at which the kinetic energy is equal to the potential energy, we can equate the two equations:

(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 h:

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

Substituting the given values, where v = 16 m/s and g = 9.8 m/s^2, we can calculate the height:

h = (1/2)(16^2) / 9.8

Calculating this expression, we find that the height at which the kinetic energy is equal to the potential energy is approximately 13.06 meters.

Therefore, the ball reaches a height of approximately 13.06 meters when its kinetic energy is equal to its potential energy.

Note: The calculations provided above are based on the given information and the equations for kinetic energy and potential energy.