An experienced pool player can control the placement of a ball after it hits an edge bumper by putting spin, or "English," on the ball. This is accomplished by aiming the cue stick so that it hits the ball either left or right of the ball's center. Suppose a player gives a ball English by hitting it to the left of center (left from his perspective).Which path in does the ball take after it collides with the bumper?Account for this behavior.

The ball will take path 'c' after colliding with the bumper.

Explanation:

If the ball is made not to spin, then it will deflect along path b

From above, If the ball spin clockwise and the point of the ball is in contact with the edge of the table stops for a moment during the collision.

Due to the angular momentum of the ball, the ball would be forced to move towards the left. The rotational velocity will be initially downward because cue  made the ball to rotate in the clockwise direction. For the ball to spin less there will be some torque acting on the ball which will cause acceleration in the counterclockwise direction.

The edge of the table produce the required acceleration.  i.e a force have to be exerted by the edge of the table on the ball with a component to the left as viewed from the player's perspective.

Therefore, the ball will take path'c' after colliding with the bumper.

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.