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 u be the velocity of projection. The equation of motion for a body at height h is given by h = ut - 1 2 gt^2 . Rearranging the terms, we get a quadratic equation in t : 1 2 gt^2 - ut + h = 0 . The roots of this equation are t₁ and t₂ , which correspond to the times at which the body is at height h during ascent and descent, respectively. From the properties of quadratic equations, the sum of the roots is t₁ + t₂ = u g/2 = 2u g . The product of the roots is t₁ t₂ = h g/2 = 2h g . The total time of flight T is th