A body is projected vertically upwards. The times corresponding to height h , while ascending and 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 vertical velocity of the body by which it is projected vertically upward. If t be the time taken by the body to reach a height h from the point of projection, then using equation of vertical motion, aligned 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 aligned It means t has two values which is already given in question, t₁= u+ u²-2 g h g aligned & and & t₂ &= u- u²-2 g h g & t₁+t₂ &= 2 u g & u &= g (t₁+t₂ ) 2 aligned