An airplane is flying in a horizontal circle at a
speed of 100 m/s. the 80.0 kg pilot does not
want the centripetal acceleration to exceed
6.92 times free-fall acceleration.
find the minimum radius of the plane’s
path. the acceleration due to gravity is 9.81
m/s2
.

the minimum radius of the plane path would be 147.45 meters.

Explanation:

given speed of the plane = 100 m/s.

and centripetal acceleration ≤ 6.92×g

we know that centripetal acceleration =

therefore

therefore

therefore r ≥ 147.54 meters

a displacement distance is size of displ

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .