A jet fighter flying at 300 m/s (just below the speed of sound) makes a turn of

Question

A jet fighter flying at 300 m/s (just below the speed of sound) makes a turn of radius 1.80 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 470 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.)

Explanation / Answer

Centripetal acceleration = v^2 / r = 300^2 / 1800 = 50 m/s^2

Now, v = 470m/s and a = v^2 / r = 10*9.81.

So, 98.1 = 470^2 / r

Or, r = 2251.8m. So, the radius, in km, of his turn = 2.25 km

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