Chapter 3 - Motion in Two or Three Dimensions - Problems - Exercises - Page 94: 3.25

A pilot will black out at a speed of 123 m/s (275 mph) or faster.

We can set the radial acceleration equal to 5.5g. $a_R = \frac{v^2}{R} = 5.5g$ $v^2 = 5.5gR$ $v = \sqrt{5.5gR} = \sqrt{(5.5)(9.80~m/s^2)(280~m)}$ $v = 123~m/s$ $v=(123~m/s)(\frac{3600s}{1609~mi})=275~mph$ A pilot will black out at a speed of 123 m/s (275 mph) or faster.