First determine how long it takes for the ball to hit the ground.
This requires only the vertical component of motion and the effect of gravity.
The ball travels 3.25 ft from the table to the floor, with an initial vertical velocity of 0.
acceleration due to gravity is approx. 32 ft/s
S = Vo t 1/2 a t^2
3.25 = 0t - 1/2 32 t^2
3.25 = -16 t^2
3.25 /16 = t^2
t ≈ 0.451 sec.
plug this time into the horizontal component of the motion.
16 = Vo * 0.451 0 acceleration
16/0.451 ≈ Vo ≈ 35.5 ft/s
35.5 * 1/5280 * 3600 ≈ 24.21 m/hr
does not beat the record.
The speed at which the ball hits the floor is a vector sum of the vertical and horizontal speeds at the moment of impact.
Vh = 35.5 ft/s
Vv = √(2*32*3.25) ≈ 14.4 ft/s
The velocity in the direction of motion is √( Vh^2 Vv^2)
√(35.5^2 14.4^2) = √ 1467.61 ≈ 38.31 ft/s