A pilot of a jet weighs 140 lbs and executes a vertical loop which in part follows the path of a cardioid whose r = 500(1+ cos q) ft. Calculate the vertical force the belt of his seat must exert on him to hold him to his seat when the plane is upside down if the constant speed at A is v = 70 ft/s.

a. 100 lbs
b. 115 lbs
c. 108 lbs
d. 120 lbs

We have r = 500(1+ cos q)

when
q = 00, r = 1000 ft


Consider the vertical forces acting on the pilot

N - 140 = (140/32.2)(-7.35)
=> N = 108 lbs

The vertical force that the belt of his seat exerts on him is 108 lbs.