A fighter pilot is practicing quick manoevers where he is pulling up out of a fa

Question

A fighter pilot is practicing quick manoevers where he is pulling up out of a fast dive where is speed is mach 2 or two times the speed of sound (=680m/s). If humans blackout when the acceleration they feel is greater than about 5 g (5 times the acceleration due to gravity), what is the radius of the circle the fighter pilot must be flying so that he doesn't blackout ? Draw the free body diagram and solve the equations for the fighter pilot at the bottom of the circle ( when he is nearest to earth).

Explanation / Answer

At the bottom of the arc, the centripetal force plus the weight would act downward

(5)(m)(9.8) = mv^2/r + mg (mass cancels)

(5)(9.8) = 680^2/r + 9.8

r = 11796 m (11.8 km)

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