As soon as a bowling ball rolls off the edge of a table its horizontal component of velocity

It will remain constant

Explanation:

The motion of the bowling ball, after it rolls off the table, is the motion of a projectile, which consists of two independent motions:

- A uniform motion (constant velocity) along the horizontal direction

- An accelerated motion (with constant downward acceleration, g=9.8 m/s^2) along the vertical direction

We are only interested in the horizontal motion: there are no forces acting along the horizontal direction (if we neglect air resistance), this means that the horizontal acceleration is zero, and therefore the horizontal component of the velocity of the ball will remain constant.

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.