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physics (mechanics)

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A running man has half the kinetic energy of a boy half his mass. The man speeds up by 1.30 m/s and then has the same kinetic energy as the boy. What is the speed (in meters/second) of the boy?

  • physics (mechanics) -

    man velocity: x
    boy velocity: b
    1/2 (2m)x^2 = 1/2 * 1/2 my^2
    4x^2 = y^2

    1/2 (2m)(x+1.3)^2 = 1/2 my^2
    2(x+1.3)^2 = 4x^2
    x^2 + 2.6x + 1.69 = 2x^2
    x^2 - 2.6x - 1.69 = 0
    x = 3.138

    check:
    1/2 (2m)*3.138^2 = 1/2 * 1/2 m*6.276^2
    9.847 = 1/2 * 19.694 = 9.847

    1/2 (2m)*4.438^2 = 1/2 m*6.276^2
    19.694 = 19.694

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