Question: The carnifowl is a bird of a unique shape

It is about 50cm long, with a wingspan of 110cm and legs only 5cm long. Its front half (chest, wings, beak) is like an eagle, though the head is feline and has cat eyes and ears. Its rear half (abdomen, tail, legs) is mostly like a turkey. However, it has paws like a dog, which have long aquiline claws. It is a carnivore, with a similar diet to an eagle. It is capable of flight

How would such a bird realistically hunt/catch its prey?

Answer: 
Like a chicken
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Flight is a very complicated thing. I look at the numbers for your bird and I see some problems in that department.

Turkeys and eagles have different proportions and different muscle and fat distribution. I don't think that this beast's center of lift will align with its center of mass when it tries to fly. Add to that: a feline head is way more massive than a bird head. You have denser bones and a bigger brain in a feline head when compared to a bird of the same approximate mass.

However, what really called my attention was this:

> 
> legs only 5cm long (...)  
> 
> it has paws like a dog
> 
> 
> 

The poor critter cannot perch, for much the same reason dogs can't.

It also won't be able to run, nor pretty much jump with such short legs. At best, if the body length of 50cm includes a long tail that is almost half of the body size, you have legs that are 20% of the animal's height. Birds of prey on the other hand have really long legs. They may not seem long when the creature is perched, or when they are tucked during flight, but a bald eagle's legs are almost as long as its body (minus the tail feathers). You can see it when whey are about to strike:

[![A picture of a bald eagle about to pounce on some prey](https://i.stack.imgur.com/x4by5.jpg)](https://i.stack.imgur.com/x4by5.jpg)

Since your bird cannot run, jump, nor even perch, it flies worse than a domesticated chicken. It will only be able fly by doing a leap of faith on a ledge, and even then it is just reducing its fall speed.

Since it is less threatening than a chick to much about every other life form, the only way it can feed on animal matter is by catching worms from the ground like a chicken.
**Like an Owl.**

The body shape you described is basically the same as an owl. The cat-like head and ears also give some resemblance to eared-owls. However you described its body as eagle like, which leads me to believe it doesn’t have sound dampening feathers reducing its overall stealth. Conversely the toe pads on its paws might serve the same role as in cats: hiding the sound of its footsteps. Which isn’t considerably useful considering it has short legs and doesn’t exactly hunt on foot.

It’s cat ears give it hearing comparable to an ordinary owl, with the key difference that they can be rotated in opposite directions. Definitely a nocturnal ambush predator.