Circular motion with decreasing speed

[bluewood]

Homework Statement

An air race pilot with 54 kg makes a vertical loop with 1200 m of radius, in such a way that the airplane's speed decreases at a constant rate.
Knowing that the airplane's seat force acting over the pilot is 1680 N at point A and 350 N at point C, determine the airplane's seat force when the airplane is at point B.

Homework Equations

The Attempt at a Solution

There are three forces acting over the object: the weight W, the centripetal force Fc and the airplane's seat force F.

I suppose at point A it's something like this:

F_c - W - F_a = 0

and at point C:

F_a - W - F_c = 0

I'm not really sure if these equations are correct. Substituting what I know I can get the speed at that points. But what should I do then to find the force acting at point B?

 

[rl.bhat]

Since the airplane's speed decreasing at a constant rate, a tangential force is acting on the pilot in the opposite direction to plane's speed. This force in not affecting on the airplane's seat force on the pilot at A and C, but it affects at B.
Seat force at A and C is given. From that you can find the velocity of the plane at A and C. From that you can find the retardation produced on the plane.