Question

Камень брошен с поверхности Земли вертикально вверх со скоростью м=12 м/c. Определите, на какой высоте его кинетическая энергия уменьшится в 2 раза. Сопротивлением движению можно пренебречь.

Answer 1

Problem Analysis

We are given that a stone is thrown vertically upward from the surface of the Earth with a velocity of 12 m/s. We need to determine the height at which its kinetic energy decreases by a factor of 2. We can solve this problem using the principles of conservation of energy.

Solution

Let's assume the initial kinetic energy of the stone is K1 and the final kinetic energy is K2. According to the principle of conservation of energy, the total mechanical energy of the stone remains constant throughout its motion.

The total mechanical energy of the stone is the sum of its kinetic energy (KE) and potential energy (PE). At the surface of the Earth, the potential energy is zero, so the total mechanical energy is equal to the kinetic energy.

At any height h, the kinetic energy of the stone is given by the formula:

KE = (1/2)mv^2

where m is the mass of the stone and v is its velocity.

Since the mass of the stone is not given, we can assume it to be 1 kg for simplicity.

Let's calculate the initial kinetic energy (K1) using the given velocity of 12 m/s:

K1 = (1/2)(1 kg)(12 m/s)^2 = 72 J

Now, we need to find the height at which the kinetic energy decreases by a factor of 2, which means the final kinetic energy (K2) is half of the initial kinetic energy (K1).

K2 = (1/2)K1 = (1/2)(72 J) = 36 J

To find the height at which the kinetic energy decreases to 36 J, we can equate the final kinetic energy to the kinetic energy at height h:

(1/2)mv^2 = 36 J

Substituting the values of m and v:

(1/2)(1 kg)(12 m/s)^2 = 36 J

Simplifying the equation:

36 J = 72 J - (1/2)(1 kg)(12 m/s)^2

36 J = 72 J - 72 J

36 J = 0 J

This equation is not possible to solve because it leads to a contradiction. It implies that the stone's kinetic energy decreases to zero before reaching any height.

Therefore, there is no height at which the stone's kinetic energy decreases by a factor of 2.

Conclusion

Based on the given information, there is no height at which the stone's kinetic energy decreases by a factor of 2. The stone's kinetic energy decreases to zero before reaching any height.