sarthak your answer is right
height = VT - V*sq.root of 2VT/g
Solution : - Take 4 cases : Case 1: Vt'=height
Case 2 : t" = V/g
Case 3 : t"' = V/g
Case 4 : t""= V' - V/g and V' = sq. root(2gh + V^2)
Now sovle these equations:-
t' + t" + t"' + t"" = T and V' = sq. root(2gh + V^2)
to get answer