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 will be (take, g as acceleration due to gravity)

Step-by-step solution

Let v be initial velocity of vertical projection and t be the time taken by the body to reach a height h from ground. Here, u=u, a=-g, s=h, t=t Using, s=u t+ 1 2 a t^2 , we have aligned & h=u t+ 1 2 (-g) t^2 & g t^2-2 u t+2 h=0 & t= 2 u 4 u^2-4 g 2 h 2 g = u u^2-2 g h g aligned It means t has two values, i.e. aligned t₁ & = u+ u^2-2 g h g t₂= u- u^2-2 g h g t₁+t₂ & = 2 u g or u= g (t₁+t₂ ) 2 aligned