Question

Pool players often pride themselves on their ability to impart a large speed to a pool ball. In the sport of billiards, event organizers often remove one of the rails on a pool table to allow players to measure the speed of their break shots (the opening shot of a game in which the player strikes a ball with his pool cue). With the rail removed, a ball can fly off the table, as shown in the figure. Pool table shown from side. Cue ball atop pool table with initial velocity V subscript 0. Trajectory of ball is across table, followed by an arc to the floor. Height of table surface is H. Distance from edge of table to point of ball's impact on floor is D. The surface of the pool table is ℎ=0.750 m from the floor. The winner of the competition wants to know if he has broken the world speed record for the break shot of 32 mph (about 14.3 m/s ). If the winner's ball landed a distance of ?=3.65 m from the table's edge, calculate the speed of his break shot ?0. Assume friction is negligible. At what speed ?1 did his pool ball hit the ground?

Answer 1

Initial horizontal launch speed,

Initial vertical launch speed,

Vertical distance to cover,

Horizontal distance covered,

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Consider the vertical motion of the cue ball

Use formula

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Use formula

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Consider the horizontal motion of the cue ball

There is no acceleration in horizontal direction, so horizontal velocity remains constant.

Horizontal velocity = horizontal distance/time

ANSWER : No, the winner of the competition did not broke the world speed record for the break shot of 32 mph (about 14.3 m/s )

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There is no acceleration in horizontal direction, so horizontal velocity remains constant.

So

Final speed,

ANSWER :

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