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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.