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What is the final velocity of mass

  1. Nov 16, 2008 #1
    1. The problem statement, all variables and given/known data
    A ball of mass 20.0kg (mass A) traveling at a initial speed of 5.0m/s, collides with a ball of mass 10.0kg (mass B) which was traveling at a initial speed of 1.0m/s. What is the final velocity of mass A, what is the final velocity of mass B?

    mA = 2mB


    2. Relevant equations
    ΣFext = 0
    Δp = 0
    ΔEk = 0
    quadratic equation


    3. The attempt at a solution
    I am unsure how to find the final velocities here because I have two variables and I have to use the quadratic equation to find the final velocities right? So I was just wondering if I could somehow isolate and get rid of a variable, this is what I have so far:

    Δp=0
    PiA + PiB = PfA +PfB
    mAviA + mBviB = mAvfA + mBvfB
    mAviA + 2mAviB = mAvfA + 2mBvfB
    viA + ViB = vfA + vfB
    (5.0) + (1.0) vfA + vfB
    6.0-vfA = vfB

    Then I put it into the kinetic energy equation and put in all the numbers and I got as an answer:

    510.0 = (20.0)(vfA)(squared) + (10.0)(vfB)(squared)

    My question is basically how am I supposed to incorporate this into the quadratic equation to find the final velocities?
     
  2. jcsd
  3. Nov 16, 2008 #2

    fluidistic

    User Avatar
    Gold Member

    Re: Momentum

    I'm not sure about what I will say but I think I'm right. It is an elastic collision.
    From the point of view of the mass B, the mass A collides at [tex]\frac{4m}{s}[/tex] and the mass B is at rest.
    So the problem remains simple. [tex]m_Av_A=m_Bv_{Bf} \Leftrightarrow v_{Bf}=\frac{m_Av_A}{m_B}=\frac{20kg\cdot 4m}{10kg\cdot s}[/tex].
    I'm not 100% sure though.
     
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