Physics Problem - Vertical Circles?

Question

A fighter pilot dives his plane toward the ground at 395m/s. He pulls out of the dive on a vertical circle. What is the minimum radius of the circle, so that the normal force exerted on the pilot by his seat never exceeds three times his weight?

Answer 1

I will assume the aircraft maintains a constant speed of 395 m/s even in the circle.

The maximum force will be at the "bottom" of the circle where the forces on the pilot are

gravity: m*g
Rotational force
m*v^2/R

according to the problem this must be equal to 3*m*g for maximum
so
3*m*g=m*v^2/R+m*g
2*g*R=v^2
R=v^2/(2*g)

=395^2/(2*9.81)
=7952 m

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