Since there is no friction, the horizontal component of velocity will not change throught the process.
so let initial velcity be u.
then horizontal component = u cos α
After time t, let velocity be v.
Now, its horizontal compnent will be v cos ß.
Since vertical velocity remains same, we get :
u cos α = v cos ß
u = v cos ß/ cos α
we have to find v.
applying linear acceleration vertically.
Initial vertical velocity: u sin α
Final vertical velocity = v sin ß
v sin ß = u sin α + a * t
v = (u sin α + a * t)/sin ß
Substitute this v in `u = v cos ß/ cos α ` and simplify.