How fighter jets can maintain lift when they do 90 degrees bank turn?

Answer 1

It's simple: they don't. If a fighter jet (or any other plane for that matter) banks to 90 degrees the plane will fall with the acceleration of gravity at that altitude. However, an observer on the ground may not perceive any elevation drop.

In the case of a fighter jet, the pilot may yaw the nose of the plane upward creating a vertical component of thrust from his (or her) engines that will counter the force of gravity to some degree. Also, the bank angle may not be exactly 90 degrees, thereby achieving a small upward component of lift from the wings as well. These combined forces may or may not be enough to overcome gravity.

Some people may argue that the centrifugal force of the banked turn will keep the jet at the same altitude. These individuals may use the example of carnival rides that, while spinning, hold you against a wall "in defiance of gravity". This is merely a principle of friction against a rigid object (the inner wall of the spinning cylinder). The centrifugal force generates enough friction against this wall that the friction overcomes gravity, not the centrifugal force. Air is obviously not rigid, so an airplane cannot generate friction enough due to centrifugal force to overcome gravity.

In essence, the plane must have a component or combination of components of forces exactly opposing gravity in order to maintain a fixed altitude.