Consider the amusement ride consisting of two circular motions. There is motion on a circle of radius 100 centered at (0,0,100) in the y, z-plane, going counter-clockwise, taking 2 pi seconds to complete a revolution. Attached to this circle of radius 5, in a plane parallel to the x,y-plane, going counter-clockwise, taking pi seconds to complete a revolution. At t=0, you enter the ride on this smaller circle at location (5,100,100). At t = pi/2, you are ejected tangentially and subject to gravitational acceleration a(t) = (0,0,-32). Where should the ground based rescue team place an air mattress? Assume the ground is the x,y-plane, z-axis up
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