A fighter pilot of mass m flies in a vertical dive through a vertical circular arc as shown. She does so at a speed such that the net force on her at point X (the lowest point of the arc) is nine times her actual weight. Her speed at X is v.
(a) Using the following figure, sketch and label all the forces on the pilot at the moment she passes through point X.
(b) Derive an expression for the normal force exerted by the seat on the pilot when she is at point X. Leave your answer in terms of m and g.
(c) Derive an expression for the radius R of the circular arc. Leave your answer in terms of v and g. (Diagram is above)
