A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is
since direction of v is opposite to the direction of g and h so from equation of motion
h=−vt+12gt2
⇒ gt2−2vt−2h=0
⇒ t=2v±√4v2+8gh2g
⇒ t=vg[1+√1+2ghv2]