A body is thrown vertically upwards at time t = 0 and it is observed at a height H at time t1 and t2 seconds during its flight. What will be the maximum height attained? (g is acceleration due to gravity)

When a body is projected vertically upwards it occupies the same position while going up and coming down after time t1 and t2 respectively.∴ H=ut−12gt2gt2−2ut+2H=0Sum of roots =t1+t2=2ug⇒u=gt1+t22∴ Hmax=u22g=gt1+t228