A projectile is fired vertically upwards with an initial velocity u. After an interval of T seconds, a second projectile is fired vertically upwards, also with initial velocity u.

For first projectile, h1=ut−12gt2 For second projectile, h2=u(t−T)−12g(t−T)2 When both meet i.e. h1=h2 :  ut−12gt2=u(t−T)−12g(t−T)2⇒ uT+12gT2=gtT⇒ t=ug+T2 and  h1=uug+T2−12gu2+T22=u22g−gT28