Question

4. Струя воды, направленная из брандспойта вертикально вверх, достигла высоты 20 метров. С какой скоростью вытекает вода из брандспойта? Сопротивление воздуха не учитывать.

Answer 1

$V= \sqrt{2gh}$=20м/сек

Answer 2

Calculation of Water Speed

To calculate the speed at which water is flowing out of the fountain, we can use the principle of conservation of energy. The potential energy of the water at the top of the fountain is converted into kinetic energy as it falls. We can equate the potential energy to the kinetic energy to find the speed of the water.

The potential energy of an object at a height h is given by the formula:

Potential Energy = mgh

Where: m = mass of the object (in this case, the mass of the water) g = acceleration due to gravity (approximately 9.8 m/s^2) h = height of the object (in this case, the height of the fountain)

The kinetic energy of an object is given by the formula:

Kinetic Energy = (1/2)mv^2

Where: m = mass of the object (in this case, the mass of the water) v = velocity of the object (in this case, the velocity of the water)

Since the potential energy is converted into kinetic energy, we can equate the two equations:

mgh = (1/2)mv^2

The mass of the water cancels out, and we are left with:

gh = (1/2)v^2

Simplifying further:

v^2 = 2gh

Taking the square root of both sides:

v = √(2gh)

Now we can substitute the given values into the equation to find the speed of the water.

Given: h = 20 meters g = 9.8 m/s^2

v = √(2 * 9.8 * 20) v ≈ 19.8 m/s

Therefore, the water is flowing out of the fountain at a speed of approximately 19.8 m/s.