Show that, under an infinitesimal change of coordinates ха — х'а %3d х" + & x"(х), ja the transformed metric satisfies gls (x) — 9aь(х) %3d— в(v, х, + v, x) to first order in

A55-kg pilot flies a jet trainer in a half vertical loop of 1200-m radius so that the speed of the trainer decreases at a constant rate. knowing that the plane has a speed of 550 km/h at point a, and the pilot experiences weightlessness at point c (i.e., the normal force from the seat bottom is zero), determine (a) the deceleration of the plane, (b) the force exerted on her by the seat of the trainer when the trainer is at point b.