How can we calculate the power output of a hummingbird's flight?

[Raziel2701]

Homework Statement

Thought it'd be easier to post the problem statement rather than writing it down again.http://imgur.com/TE2kN.png"

The Attempt at a Solution

I'm trying to get b and c.

For b I have: \frac{mgd}{\Delta t_{one flap}}=\frac{\frac{1}{2}m(v_f ^2 -v_i ^2)}{\Delta t}

The masses cancel but then I have a mess of symbols that don't necessarily make it clear to me how I would go about rearranging this so that I can see mathematically what the answer to part a is.

For part c, so work would be force times displacement. Now the force the bird exerts on the wind is the one responsible for the bird's flight. I want to find the work done by the hummingbird on the air, and I think it could be done since I have the displacement of the air, and I have it's mass, I just don't have its acceleration and I was wondering if the force exerted by the hummingbird is actually just mg, the weight of the hummingbird?

If that was the case however, I would need a time interval to divide the work, and so I think I may have to use the equation I derive from part b, to answer part c.

Any insights?

 

[willem2]

For b, you have to use conservation of momentum first to find out how many flaps/sec the kolibri makes and what the velocity of the air is that it pushes downwards

(flaps per second) * (down ward momentum of the air in each flap) must equal the force of gravity.
After that you can find out the kinetic energy of the air in each flap and the average power of the bird.

 

[Raziel2701]

I don't see it, where exactly is momentum being conserved? If I just set mv_i= mv_f I don't really go very far...