A child A is swinging from a swing that is attached to a trolley that is free to move along a fixed rail. Letting L = 3.2 m, if at a given instant { a }_{ B } = 3.4m/{ s }^{ 2 },\theta =23° , \dot { \theta } = 0.45 rad/s, and \ddot { \theta } = -0.2 rad/{ s }^{ 2 }, determine the magnitude of the acceleration of the child relative to the rail at that instant.