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 = V₀ 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 V₀=980 km/h and g=9.81 m/s² O.