Physics question

Question

What is the minimum radius at which an airplane flying at 300. m/s can make a U-turn if its centripetal acceleration is NOT to exceed 4 g’s (1g = 9.8m/s2)?

Answer 1

Let

v = 300 m/s be the airplane's velocity,

g = 9.8 m/s² be gravitational acceleration,

a <= 4g be the maximum centripetal acceleration,

r (to be bounded) be the radius of the plane's turn.

The expression for centripetal acceleration is

a = v²/r

Applying the given bound

v²/r <= 4g

Simplifying

r >= v²/4g

Substituting actual numbers

r >= 300²/4x9.8 = 2,296m