Answer:
2296 m
Explanation:
Since the pilot is flying in a loop (circular motion), there is centripetal force acting on him.
The centripetal force at any point during the motion is the result of the combined action of the force of gravity ([tex]mg[/tex]) and the normal reaction ([tex]N[/tex]). However, here we are told that when the plane is upside-down, the pilot feels weightless: this means that the normal reaction is zero,
N = 0
So the gravitational force entirely provides the centripetal force, so we can write:
[tex]mg=m\frac{v^2}{r}[/tex]
where
m = 80 kg is the mass of the pilot
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
v = 150 m/s is the speed of the pilot
r is the radius of the loop
And solving for r, we can find the radius of the loop:
[tex]r=\frac{v^2}{g}=\frac{150^2}{9.8}=2296 m[/tex]
