Question

Камень массой 2 кг брошен вертикально вверх, его начальная кинетическая энергия 400 Дж. Какой будет его скорость на высоте 15 метров?

Answer 1

Ек = 400 Дж
часть кин.энергии перейдет в потенц.
потенциальная энергия на высоте h =15 м
Еп= mgh =2*10*15 =300 Дж
значит останется еще Eк(15) = 400 -300 =100 Дж
тогда скорость будет
Ек(15) = mv^2/2
v =√2Ек(18)/m = √2*100/2 = √100 = 10 м/с
ОТВЕТ 10 м/с

Answer 2

Calculation of Velocity at 15 Meters Height

To determine the velocity of a 2 kg stone at a height of 15 meters, we can use the principle of conservation of energy. The initial kinetic energy of the stone is given as 400 J.

According to the principle of conservation of energy, the total mechanical energy of the stone remains constant throughout its motion. This means that the initial kinetic energy of the stone is equal to the sum of its potential energy at a height of 15 meters and its final kinetic energy at that height.

Mathematically, we can express this as:

Initial Kinetic Energy = Potential Energy at 15 meters + Final Kinetic Energy at 15 meters

The potential energy at a height of 15 meters can be calculated using the formula:

Potential Energy = mass * acceleration due to gravity * height

Given that the mass of the stone is 2 kg and the height is 15 meters, we can substitute these values into the formula to find the potential energy at 15 meters.

Now, let's calculate the potential energy at 15 meters using the given values:

Potential Energy = 2 kg * 9.8 m/s^2 * 15 m

Using the above formula, we find that the potential energy at 15 meters is 294 J.

Next, we can rearrange the equation for the conservation of energy to solve for the final kinetic energy at 15 meters:

Final Kinetic Energy at 15 meters = Initial Kinetic Energy - Potential Energy at 15 meters

Substituting the given values into the equation, we have:

Final Kinetic Energy at 15 meters = 400 J - 294 J

Calculating the above expression, we find that the final kinetic energy at 15 meters is 106 J.

Finally, we can use the formula for kinetic energy to calculate the velocity of the stone at 15 meters:

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

Rearranging the equation to solve for velocity, we have:

Velocity = sqrt((2 * Final Kinetic Energy) / mass)

Substituting the values into the equation, we get:

Velocity = sqrt((2 * 106 J) / 2 kg)

Calculating the above expression, we find that the velocity of the stone at a height of 15 meters is approximately 10.39 m/s.

Therefore, the velocity of the stone at a height of 15 meters is approximately 10.39 m/s