A body is projected vertically upwards at time t=0 and it is seen at a height H at time t₁ and t₂ second during its flight. The maximum height attained is ( g is acceleration due to gravity)

Step-by-step solution

Let time taken by the body to fal from point C to B is t^ . Then t₁+2 t^ =t₂ t^ = ( t₂-t₁ 2 ) ( i ) Total time taken to reach point C aligned T & =t₁+t^ & =t₁+ t₂-t₁ 2 & = 2 t₁+t₂-t₁ 2 & = ( t₁+t₂ 2 ) aligned Maximum height attained aligned H_ & = 1 2 g(T)^2 & = 1 2 g ( t₁+t₂ 2 )^2 & = 1 2 g (t₁+t₂ )^2 4 H_ & = 1 8 g (t₁+t₂ )^2 ~m aligned