Question

When a fighter pilot makes a very quick turn, he experiences a centripetal acceleration. When this acceleration is greater than about

8 ⨯ g, the pilot will usually lose consciousness ("black out"). Consider a pilot flying at a speed of 826 m/s (about 1848 mi/h) who wants to make a very sharp turn. What is the minimum radius of curvature he can take without blacking out?

Answer 1

You don't give units for the aircraft's speed but if I use 826 meters per second
(which is a very fast airplane) I get the same answer you did, 8702.5 meters.
We know the maximum acceleration he can take is 8 Gs, and G = 9.8 m/sec²
so a cannot exceed 9.8 times 8, or 78.4 meters per second per second.
We know a = s²/r, therefore r = s²/a = (826)²/78.4 = 8702.5 meters.
Are you sure you have the correct units for the speed? 826 meters per second
is extremely fast. If it is 826 miles per hour
you would need to convert that to meters per second and put that value into
your formula.