A marble is fired horizontally from a launching device attached to the edge of a tabletop which is 94.0 cm above the floor. The marble then strikes the floor 2.35 meters from the edge of the table. Show your work please.

Choose the plane coordinates system centered at the initial position of the marble with the x-axis directed to the right and the y-axis directed downwards.

Let x, y be the coordinates of the point where the marble hit the floor and t be the time when it happened.

Given: x = 2.35 m, y = 94.0 cm = 0.940 m, g = 9.81 m/s^2.

Find the initial velocity v.

From the equations x = vt and y = gt^2/2 we find t = sqrt{2y/g} and v = x/t = x sqrt{g/2y} =