Question

Камень бросили с высоты 15 м вертикально вниз со скоростью 5м/с.Применяя закон сохранения энергии,найдите скорость,с которой камень ударился о землю?

Answer 1

Решение на фотографии

Answer 2

Calculation of the Final Velocity of the Stone

To find the final velocity with which the stone hits the ground, we can apply the principle of conservation of energy. According to this principle, the total mechanical energy of a system remains constant if no external forces are acting on it.

In this case, the stone is dropped vertically from a height of 15 m with an initial velocity of 5 m/s. We need to find the final velocity when it hits the ground.

The total mechanical energy of the stone can be expressed as the sum of its potential energy (PE) and kinetic energy (KE):

PE + KE = Constant

At the initial position, when the stone is dropped, its potential energy is maximum and its kinetic energy is zero. At the final position, when the stone hits the ground, its potential energy is zero and its kinetic energy is maximum.

Therefore, we can write the equation as:

mgh + (1/2)mv^2 = (1/2)mvf^2

Where: - m is the mass of the stone (which we assume to be constant) - g is the acceleration due to gravity (approximately 9.8 m/s^2) - h is the initial height (15 m) - v is the initial velocity (5 m/s) - vf is the final velocity (which we need to find)

Simplifying the equation, we get:

mgh = (1/2)mvf^2 - (1/2)mv^2

Since the mass of the stone cancels out, we can further simplify the equation to:

gh = (1/2)vf^2 - (1/2)v^2

Now, let's substitute the given values into the equation and solve for vf.

g = 9.8 m/s^2 h = 15 m v = 5 m/s

9.8 * 15 = (1/2)vf^2 - (1/2)5^2

Simplifying further:

147 = (1/2)vf^2 - 12.5

(1/2)vf^2 = 147 + 12.5

(1/2)vf^2 = 159.5

vf^2 = 159.5 * 2

vf^2 = 319

Taking the square root of both sides:

vf = √319

vf ≈ 17.85 m/s

Therefore, the final velocity with which the stone hits the ground is approximately 17.85 m/s.

Please note that the above calculation assumes no air resistance and that the stone is dropped vertically without any horizontal motion.