Answer:
What forces act on the ball in the horizontal direction as it rolls? None. So that means there is no horizontal acceleration and therefore the horizontal component of the ball's speed is constant.
And since the ball was only travelling horizontally at the instant it rolled off the table, initially the vertical component of its speed is 0. That means the time taken to hit the ground after rolling off the table is the same as if it was just dropped 0.950 m. We can find this time using one of the kinematic equations of motion in the vertical direction, taking downwards as positive. Then we have the following information:
u = initial velocity = 0 m/s
d = distance fallen = 0.950 m
a = acceleration (due to gravity) = 9.8 m/s²
t = time = ?
d = ut + 1/2 at². Since u = 0 this reduces to d = 1/2 at² and rearranges to t = √(2d/a) = √(2*0.95/9.8) = 0.4403 s.
In the same amount of time, the ball travels a horizontal distance of 0.352 m. We already know the horizontal velcoity is constant, so horizontal velocity is just horizontal distance divided by time = (0.352 m)/(0.4403 s) = 0.799 m/s.