Physics behind a fan based flying car concept

[PMsacr0sanct]

Homework Statement

For decades, people have dreamed of cars that can fly. You are part of a team which hopes
to build the worldʼs first commercial flying car.
Your proposed design has four fans, each of radius 50cm. Each fan sucks in air from above
the car and blows it downwards. The downward flow of air can be approximated as a column
of radius equal to that of the fan, traveling at a uniform speed downwards.

How fast must the air be blown downwards if the car plus passengers weigh 1000 kg?
You may assume that the density of air is 1.2 kg m-3.

Homework Equations

The Attempt at a Solution

I have considered pressure differences, and conservation of angular momentum, but I can't seem to apply them in any way that helps me solve for the required unknown.

 

[tms]

Perhaps if you thought of the car as a rocket.