Stunt pilots and fighter pilots who fly at high speeds in a downward-curving arc
ID: 1982554 • Letter: S
Question
Stunt pilots and fighter pilots who fly at high speeds in a downward-curving arc may experience a “red out,” in which blood is forced upward into the flier’s head, potentially swelling or breaking capillaries in the eyes and leading to a reddening of vision and even loss of consciousness. This effect can occur when the non-gravitational part of the centripetal acceleration exceeds 2.5’s.For a stunt plane flying at a speed of 430 , what is the minimum radius of downward curve a pilot can achieve without experiencing a red out at the top of the arc? (Hint: Remember that gravity provides part of the centripetal acceleration at the top of the arc; it’s the acceleration required in excess of gravity that causes this problem.)
Explanation / Answer
Net centripetal acceleration is: an = v2 /r
It can be written as g + x.
Hence the non gravitational part of the acceleration is = (v2 /r) - g
and this cannot exceed 2.5 x 9.8m/s/s = 24.5m/s/s
v = 430km/h = 119.44m/s, so we have
v2 /r -g = 24.55
v2 /r = g +24.55 = 34.35
34.35m/s/s = (119.44m/s)^2 / r
r = (119.44m/s)^2/34.35 m/s/s = 415.34 m (approx)
It seems the problem should be done this way. But still am unable to get the exact answer (as you said that the answer is 420). Apart from this I don't see any other way to solve it.