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Work -- KE related Question

  1. Jan 25, 2017 #1
    1. The problem statement, all variables and given/known data
    A father racing his son has half the kinetic energy of the son,who has half the mass of the father.The father speeds up by ##1.0\frac {m} {s}## and then has the same kinetic energy as the son.What are the original speeds of (a)the father and (b) the son

    2. Relevant equations
    ##E_k=\frac 1 2 mv^2##

    3. The attempt at a solution
    ##m_f=2m_s##
    ##2E_f=E_s##

    İnital situation;
    ##2E_f= m_f(v_{f_0})^2=E_s=\frac 1 2 m_s(v_{s_0})^2##

    so
    ##m_f=2m_s##

    then we will obtain ##4(v_{f_0})^2=(v_{s_0})^2##

    Final situation

    ##\frac 1 2 m_f(v_{f_0}+1)^2=\frac 1 2 m_s(v_{s_0})^2##

    then I get ##v_{f_0}=1\frac {m} {s}## which book says its ##2.4\frac {m} {s}##

    Where I am going wrong ? (My native language is not english so If made a mistake in understanding the question so sorry )

    Thanks
     
    Last edited: Jan 25, 2017
  2. jcsd
  3. Jan 25, 2017 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Everything looks good here. Show how you got your answer.
     
  4. Jan 25, 2017 #3
    ##\frac 1 2 m_f(v_{f_0}+1)^2=\frac 1 2 m_s(v_{s_0})^2##

    we know that

    ##m_f=2m_s##
    so
    ##\frac 1 2 2m_s(v_{f_0}+1)^2=\frac 1 2 m_s(v_{s_0})^2##

    then we get ;

    ##2m_s(v_{f_0}+1)^2=m_s(v_{s_0})^2##

    ##2(v_{f_0}+1)^2=(v_{s_0})^2## (1)

    ##\frac {(v_{s_0})^2} 2=2(v_{f_0})^2## (2) From the ##4(v_{f_0})^2=(v_{s_0})^2##

    lets put this ##Eq_2## in the ##Eq_1##

    ##(v_{f_0}+1)^2=2(v_{f_0})^2##

    ##(v_{f_0})^2+2(v_{f_0})+1=2(v_{f_0})^2##

    ##(v_{f_0})^2-2(v_{f_0})-1=0##

    ##((v_{f_0})-1)^2=0##

    ##(v_{f_0})=1\frac {m} {s}##
     
  5. Jan 25, 2017 #4

    Doc Al

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    Staff: Mentor

    This is where you're messing up.
     
  6. Jan 25, 2017 #5
    Oh I see.Thanks.unbelievable....
     
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