If you launch a marble out of a launcher on a table with a given angle, and you know that range( distance it travelled) and time travelled ( if needed). The only force acting upon is gravity. How would you find the initial speed or velocity of the launcher? Is there a formula?

x = vo t + 1/2 at^2

is used most for projectile motion.
vo sin(theta) gives initial y velocity
vo cos(theta) gives initial x velocity

It depends on what they give you as far as the problem goes