Answer:
F=92838 N
θ = 18.5°
Explanation:
F: lift force
θ: banking angle of the airplane, clockwise from vertical
W: weight of the airplane
v: velocity of the airplane
m = 8970 kg
R = 8.45 miles = 13598.96 meters
T = 0.112 hours = 403.2 seconds
g = 9.81 m/s^2
Fy = F*cos(θ)
Fx = F*sin(θ)
W = m*g
v = 2*pi*R/T (velocity = distance/time) =2*pi*13598.96m/403.2 sec
v=211.8 m/s
As the airplane is in level flight,
ΣFy = 0 = Fy - W
> Fy = m*g =(8970*9.81)N
Fy=87995.7
F_cent = m*v^2/R = Fx =8970 kg*211.8 m/s^2 /13598.96m
Fx = m*(2*pi*R/T)^2 / R = 29592N
> Fx = 4*pi^2*m*R/(T^2)
The magnitude of the lift force is
F = sqrt(Fx^2 + Fy^2)
F=sqrt(29592 N^2+87995.7^2)
>> F = 92838 N
The angle of the banking will be
θ = atan(Fx/Fy)
θ=atan(29592N/87995.7N)
>> θ = 18.5°
