A jet fighter flying at 300 m/s (just below the speed of sound) makes a turn of radius 2.55 km.   (a)What is its centripetal acceleration in gs?   (b)Suppose the pilot makes an emergency turn to avoid an approaching missile, subjecting himself to a centripetal acceleration of 10 gs, while flying at 400 m/s (supersonic). What is the radius, in km, of his turn? (This must be short-lived because fighter planes can only briefly endure such large accelerations without serious damage, and the pilot will soon black out at 10 gs.)

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A jet fighter flying at 300 m/s (just below the speed of sound) makes a turn of radius 2.55 km.
 
(a)What is its centripetal acceleration in gs?
 
(b)Suppose the pilot makes an emergency turn to avoid an approaching missile, subjecting himself to a centripetal acceleration of 10 gs, while flying at 400 m/s (supersonic). What is the radius, in km, of his turn? (This must be short-lived because fighter planes can only briefly endure such large accelerations without serious damage, and the pilot will soon black out at 10 gs.)
Expert Solution
Step 1

a)

Given,

The speed of the fighter jet = v = 300m/s

Radius of the turn = r = 2.55km = 2.55×103m

We know that,

 Centripetal acceleration (a) is given by,

a= v²/r

Substituting know values,

a = 300²/(2.55×10³)

a = 35.29411764 m/s² is the required centripetal acceleration.

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