Question

Тело брошено вертикально вверх со скоростью 20 м/с. На какой высоте его кинетическая энергия уменьшится в 4 раза?

Answer 1

Дано  V=20m/c       E2=E1/4     h-?
по закону сохранения энергии E1 =E1/4+m*g*h
m*g*h=3*m*V^2/4
h=3*V^2/4*g=3*20*20/4*10=30 м

Answer 2

Answer:

To find the height at which the kinetic energy of the body decreases by 4 times, we can use the formula for kinetic energy and gravitational potential energy.

The initial kinetic energy (KE) of the body is given by the formula: KE = 0.5 * m * v^2.

The initial potential energy (PE) of the body at height h is given by the formula: PE = m * g * h.

When the body reaches a certain height, its kinetic energy decreases by 4 times. Let's denote this height as h1.

The final kinetic energy at height h1 is given by: KE1 = 0.5 * m * v1^2.

Calculation:

Given: Initial velocity, v = 20 m/s Initial kinetic energy, KE = 0.5 * m * v^2 The kinetic energy decreases by 4 times at height h1.

Using the given information, we can calculate the height at which the kinetic energy decreases by 4 times.

Let's denote the final velocity at height h1 as v1.

We know that kinetic energy is proportional to the square of the velocity, so if the kinetic energy decreases by 4 times, the velocity will decrease by 2 times.

So, the final velocity at height h1, v1 = v/2 = 20/2 = 10 m/s.

Now, we can calculate the height at which the kinetic energy decreases by 4 times using the given information and the formulas for kinetic energy and potential energy.

Solution:

The initial kinetic energy (KE) is given by: KE = 0.5 * m * v^2 = 0.5 * m * 20^2 = 200m.

The final kinetic energy (KE1) when the velocity is 10 m/s is given by: KE1 = 0.5 * m * v1^2 = 0.5 * m * 10^2 = 50m.

We are looking for the height at which the kinetic energy decreases by 4 times, so: KE1 = 0.25 * KE.

Equating the initial and final kinetic energies: 0.25 * 200m = 50m.

Solving for m: m = 50m / 0.25 = 200m.

Now, we can calculate the height using the formula for potential energy: PE = m * g * h.

Substituting the value of m and rearranging the formula: h = PE / (m * g).

Given that g (acceleration due to gravity) is approximately 9.81 m/s^2, we can calculate the height h at which the kinetic energy decreases by 4 times.

Final Calculation:

h = PE / (m * g) = 200m * 9.81 / 200m = 9.81 m.

So, the height at which the kinetic energy of the body decreases by 4 times is approximately 9.81 meters.