B9 (a) A cannon ball is shot up from the ground at an angle 0 to the horizontal as shown in Figure B9(a). The horizontal distance and the vertical distance from O against time, t, are governed by the following equations respectively: x = u cos(0) t yu sin(0) t- 0.5 g t (Hint: u, 0 and g are constant parameters) Determine: dy (i) in terms of x, u, 0 and g; and (5 marks) dx (ii) the maximum height of cannon ball attained. (5 marks) y+ Ymax u Figure B9(a) (b) Fresh water is pumped into a storage tank. The pumping rate of the water can be described by =t3 m/min, where V is the dv dt volume of water in the storage tank in cubic meter and t is the time in minutes. (i) Find the volume of water in the tank after t minutes. Given that the initial condition is V=0 when t=0. (6 marks) (ii) If the capacity of the tank is 150 m, find the time needed to fill up the empty storage tank. Correct your answer to 3 significant figures. (4 marks)