Physics

A blue billiard ball with mass m crashes into a red billiard ball with the same mass that is at rest. The collision results in the blue billiard ball travelling with a velocity of v and the red billiard ball with a velocity of 3V. In terms of v and m determine the blue billiard ball's velocity before the collision.

asked by Student12
  1. Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B.

    We know that he is in the water for d/(v/3) = 3d/v seconds, so
    y = 3d/v * v = 3d.

    His path is thus

    √(d^2+x^2) meters on land,
    d meters in the water,
    √((2d)^2+(x-3d)^2) meters on land to B

    Now, dividing distance by speed, his time to travel is

    t = 1/(3v) (√(d^2+x^2)+√((2d)^2+(x-3d)^2)) + 3d/v
    =
    √(d^2+x^2)+√(x^2-6dx+13d^2)+9d
    --------------------------------------
               3v

    posted by Steve
  2. Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B.

    We know that he is in the water for d/(v/3) = 3d/v seconds, so
    y = 3d/v * v = 3d.

    His path is thus

    √(d^2+x^2) meters on land,
    d meters in the water,
    √((2d)^2+(x-3d)^2) meters on land to B

    Now, dividing distance by speed, his time to travel is

    t = 1/(3v) (√(d^2+x^2)+√((2d)^2+(x-3d)^2)) + 3d/v
    =
    √(d^2+x^2)+√(x^2-6dx+13d^2)+9d
    ---------------------------------------------
                      3v

    posted by Steve

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