The ball rolls off the horizontal dinner table with an initial velocity of 2.45 m/s in the horizontal direction. It strikes the floor with a horizontal displacement of 1.3 m.
Let the height of the table be h. The horizontal velocity of the ball does not change as the ball drops to the ground from the table. The time taken by the ball to travel a distance of 1.3 m is 1.3/2.45 = 26/49 seconds.
The vertical distance traveled by the ball in 26/49 seconds is 0*(26/49) + (1/2)*9.8*(26/49)^2 = `338/245 ~~` 1.37 m
The height of the table is approximately 1.37 m