Question

С поверхности земли вертикально вверх бросили камень со скоростью 20 м/с. На какой высоте кинетическая энергия камня уменьшится в 5 раз?

Answer 1

Mv^2/2=mgh+(m2v2/2)5
(100-20)/20=4
H=4

Answer 2

Calculation of the Height at which the Kinetic Energy of the Stone Decreases by 5 Times

To calculate the height at which the kinetic energy of the stone decreases by 5 times, we need to use the formula for kinetic energy:

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

Given that the stone is thrown vertically upwards with an initial velocity of 20 m/s, we can calculate the initial kinetic energy.

Let's assume the mass of the stone is 1 kg for simplicity.

Initial Kinetic Energy (KE0) = (1/2) * mass * velocity^2 = (1/2) * 1 kg * (20 m/s)^2 = 200 J.

To find the height at which the kinetic energy decreases by 5 times, we can use the conservation of mechanical energy. At the highest point of the stone's trajectory, all of its initial kinetic energy will be converted into potential energy.

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

We can equate the initial kinetic energy to the potential energy at the highest point:

KE0 = PE = mass * gravity * height.

Rearranging the equation, we can solve for the height:

height = KE0 / (mass * gravity).

Substituting the values, we get:

height = 200 J / (1 kg * 9.8 m/s^2) = 20.41 meters.

Therefore, the height at which the kinetic energy of the stone decreases by 5 times is approximately 20.41 meters.