A stone is thrown vertically upward with an initial speed u from ground level. Neglect air resistance.
a. (i) Show that the total time of flight until the stone returns to the point of projection is g2u.
b. (ii) Prove that the maximum height H reached by the stone is 2gu2.
c. (iii) If the stone is required to stay in the air for exactly 6s, calculate the initial speed that must be imparted and the corresponding maximum height attained.