![1372_fri.png](https://secure.tutorsglobe.com/CMSImages/1372_fri.png)
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.
![820_pilot.png](https://secure.tutorsglobe.com/CMSImages/820_pilot.png)
(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)
![1125_friction.png](https://secure.tutorsglobe.com/CMSImages/1125_friction.png)