The airplane shown in the figure is to achieve "weightlessness" for a short period of time by flying along a curved path such that it's acceleration components in x direction a_{x} = 0 and in y direction a_{y} = -g. If the velocity of the plane in x - direction V_{x} = V_{0} and y-direction V_{y}=0 at the time t=0 and plane is at point O.
(i) Derive a tangential acceleration of the plane a_{t} as function of time t.
(ii) Derive a normal acceleration of the plane as a function of time t
(iii) Calculate the tangential acceleration and the normal acceleration after time t= 5 sec, if V_{0}=980 km/h and g=9.81 m/s^{2} O.