Science, Physics, math, calculus

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Pool players often pride themselves on their ability to impart a large speed on 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 0.770 m from the floor. The placement of the tape is such that 0 m aligns to 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). The ball landed a distance 5.15 m from the table edge, calculate his break shot speed.

At what speed did his pool ball hit the ground?

  • Science, Physics, math, calculus -

    a. h = 0.5g*t^2 = 0.77
    4.9t^2 = 0.77
    t^2 = 0.1571
    t = 0.396 s. = Fall time.
    Dx = Xo * t = 5.15 m.
    Xo * 0.396 = 5.15
    Xo = 13 m/s = Break speed.

    b. V^2 = Vo^2 + 2g*h
    V^2 = 0 + 19.6*0.77 = 15.09
    V = 3.88 m/s

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