A ball is thrown upwards with a speed u from a height h above the ground. The time taken by the ball to hit the ground is

Time taken to reach the highest point from the height h is obtained from equation, v = u - gt ∴                           0=u-gt1 or t1=ug                                           (∵ At highest point, final velocity of ball = 0)Height attained above h is obtained from v2 - u2 = 2 (-g)h1or               0-u2=2(-g)h1 or h1=u22gTotal height, h2=h1+h=u22g+hTime taken to hit the ground is obtained from                     h2=ut+12at2 or u22g+h=0+12gt22 ∴   , t2=u2+2ghg2 Therefore , total time , T = t1+t2 =ug[1+1+2ghu2]