Power required the support a helicopter

[Doyouevenlift]

A rescue helicopter of mass 810 kg, supports itself in a stationary position by imparting
a downward velocity, v, to the air in a circle of radius 4.0 m. The density of the air is
1.20 kg m-3.

Calculate:
(i) the value of v
(ii) the power, P, required to support the helicopter

So, I do have the solution to part one, which is 11.5 ms-1. However, the solution for ii eludes me. The answer sheet does something weird:

Power = 0.5(pi*4^2)(1.2)v^3. From the first term I'm guessing they're using E=.5mv^2, but why is the velocity raised to the third?

 

[voko]

"I'm guessing" is not the way to solve problems in physics.

This problem can be solved by using the impulse-momentum equation.

 

[Doyouevenlift]

"I'm guessing" is not the way to solve problems in physics.

This problem can be solved by using the impulse-momentum equation.

That's why I asked it, you arrogant person.

 

[voko]

I do not think I was or am being arrogant. I pointed out that guessing how the problem is solved from the answer, as you tried to, is almost never productive.

On the other hand, you did not demonstrate any other attempt at solving the problem, as is required in this forum.

 

[Doyouevenlift]

I do not think I was or am being arrogant. I pointed out that guessing how the problem is solved from the answer, as you tried to, is almost never productive.

On the other hand, you did not demonstrate any other attempt at solving the problem, as is required in this forum.

My attempt was just using kinetic energy, and my question was why the answer sheet has taken velocity to the third power, which hasn't been answered yet.

 

[voko]

What is the total mass of the air propelled by the helicopter in one second? What is the kinetic energy of that mass?