The given situation is shown in the following figure.
If time taken by the ball to reach at highest point A is t, then 0=v−gt⇒t=gV
Total time taken to reach the ball from point of projection to reach at point B is given as t1=t+t=2t⇒t1=g2v
If t2 be the time taken by the ball to reach from point B to point C, then h=vt2+21gt22 ⇒gt22+2vt2−2h=0 ∴t2=2g−2v±4v2+8gh t2=g−v+2v2+2gh
[taking + ve sign because time is positive] ∴ Total time, T=t1+t2=g2v−gv+2v2+2gh =gv+gv1+v22gh=gv[1+1+v22gh]