A baseball rolls off of a .7 m high desk and strikes the floor .25 m always how fast was the ball rolling

the ball's velocity was approximately 0.66 m/s

Explanation:

Recall that we can study the motion of the baseball rolling off the table in vertical component and horizontal component separately.

Since the velocity at which the ball was rolling is entirely in the horizontal direction, it doesn't affect the vertical motion that can therefore be studied as a free fall, where only the constant acceleration of gravity is affecting the vertical movement.

Then, considering that the ball, as it falls covers a vertical distance of 0.7 meters to the ground, we can set the equation of motion for this, and estimate the time the ball was in the air:

0.7 = (1/2) g t^2

solve for t:

t^2 = 1.4 / g

t = 0.3779  sec

which we can round to about 0.38 seconds

No we use this time in the horizontal motion, which is only determined by the ball's initial velocity (vi) as it takes off:

horizontal distance covered = vi * t

0.25 = vi * (0.38)

solve for vi:

vi = 0.25/0.38  m/s

vi = 0.65798  m/s

Then the ball's velocity was approximately 0.66 m/s

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be