Question

In: Physics

Pool players often pride themselves on their ability to impart a large speed to a pool...

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 the only participant with a physics background, they have placed you in charge of determining the speed of the players\' break shots.

The top of the pool table is 0.730 m from the floor. The placement of the tape is such that 0 m is aligned with the edge of the table (as shown). The winner of the competition wants to know if he has broken the world record for the break shot of 32 mph (about 14.3 m/s). If the winner\'s ball landed a distance 4.25 m from the table edge, calculate his break shot speed.

At what speed did his pool ball hit the ground?

Expert Solution

First you must know that that is a parabolic movement.

We consider the ground as the reference point.

All vector and pointing upward and the horizontal direction of the ball as positive.

we calculate the time it takes to drop the ball down to the following equation.

Vertical component of the velocity which is initially zero. because the ball has only horizontal speed when leaving the table.

Initial height measured from the ground.

acceleration of gravity, which is negative because it points toward the ground.

We evaluate the equation when it comes to ground ie

we have the expression for time and calculate.

breaking speed corresponds to the horizontal velocity component, which remains constant in this type of movement and is calculated as:

The winner did not break anything :(

To calculate the speed reaching the ground vertical velocity component is calculated.

vectorially speed we can write so.

Calculating the modulus of the velocity vector to reach the ground ..

genius_generous answered 1 year ago

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