A body is projected vertically upwards. The times corresponding to height h , while ascending and while descending are t₁ and t₂ , respectively. Then, the velocity of projection is ( g is acceleration due to gravity)

Step-by-step solution

Let u be the initial velocity of vertical projection and t be the time taken by the body to reach at height h from the ground. Using equation, h=u t+ 1 2 a t² Here, u=u, a=-g h=u t- 1 2 g t² g t²-2 u t+2 h=0 t= 2 u 4 u²-4 g 2 h 2 g = u u²-2 g h g It means t has two values, t₁ and t₂ . Where, t₁ is time taken by the body in reaching maximum height and t₂ be the time taken by the body in reaching ground from maximum height. aligned & t₁= u+ u²-2 g h g & and t₂= u- u²-2 g h g & t₁+t₂= 2 u g or u= g (t₁+t₂ ) 2 aligned